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The modes delivered by proper orthogonal decomposition (POD) are uncorrelated as per definition; but interestingly, they are not necessarily independent in terms of spatio-temporal flow-pattern dynamics. For instance, periodic structures that travel as waves through a series of snapshots often consist of pairs of modes with harmonic functions shifted 90 degree in phase and/or a spatial offset by a quarter of the spatial wave length of the convective flow pattern. Identification of such pairs, however, largely builds upon experience, visual inspection and/or the analysis of the reconstructed coefficients in cyclograms (Lissajous figures). This effort becomes even more challenging if measurement noise or other spurious information contaminates the raw data under consideration. One possibility to automatically pair corresponding patterns with common POD algorithms is the immediate application of the POD method to complex data (see Pfeffer et al., 1990). As outlined by Horel (1984), the Hilbert transform is a well-known and straight forward means to obtain the required extension of the original signal with an appropriate 90 degrees phase shift, which is independent of the fundamental frequencies. The complex extension of the original (real) signal Xi and its (discrete) Hilbert transform HT{Xi} as the imaginary part Xi +iHT{Xi} with the imaginary unit i is commonly known as the so-called analytical signal.

Vertical-axis wind turbines (VAWTs) are being reconsidered as a complementary technology to the more widely used horizontal-axis wind turbines (HAWTs) due to their unique suitability for offshore deployments. In addition, field experiments have confirmed that vertical-axis wind turbines can interact synergistically to enhance the total power production when placed in close proximity. Here, we use an actuator line model in a large-eddy simulation to test novel VAWT farm configurations that exploit these synergistic interactions. We first design clusters with three turbines each that preserve the omni-directionality of vertical-axis wind turbines, and optimize the distance between the clustered turbines. We then configure farms based on clusters, rather than individual turbines. The simulations confirm that vertical-axis wind turbines have a positive influence on each other when packed in well-designed clusters: such configurations increase the power generation of a single turbine by about 10 percent. In addition, the cluster designs allow for closer turbine spacing resulting in about three times the number of turbines for a given land area compared to conventional configurations. Therefore, both the turbine and wind-farm efficiencies are improved, leading to a significant increase in the density of power production per unit land area.

From Lie-group (symmetry) analysis of the multi-point correlation equation Oberlack and Gunther (Fluid Dyn Res 33:453-476, 2003) found three different solutions for the behavior of shear-free turbulence: (i) a diffusion like solution, in which turbulence diffuses freely into the adjacent calm fluid, (ii) a deceleration wave like solution when there is an upper bound for the integral length scale and (iii) a finite domain solution for the case when rotation is applied to the system. This paper deals with the experimental validation of the theory. We use an oscillating grid to generate turbulence in a water tank and Particle Image Velocimetry (PIV) to determine the two-dimensional velocity and out-of-plane vorticity components. The whole setup is placed on a rotating table. After the forcing is initiated, a turbulent layer develops which is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/non-turbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid. We measure the propagation of the TNTI and find quantitative agreement with the predicted spreading laws for case one and two. For case three (system rotation), we observe that there is a sharp transition between a 3D turbulent flow close to the source of energy and a more 2D-like wavy flow further away. We measure that the separation depth becomes constant and in this sense, we confirm the theoretical finite domain solution.

Experimental results from three different full scale arrays of vertical-axis wind turbines (VAWTs) under natural wind conditions are presented. The wind velocities throughout the turbine arrays are measured using a portable meteorological tower with seven, vertically staggered, three-component ultrasonic anemometers. The power output of each turbine is recorded simultaneously. The comparison between the horizontal and vertical energy transport for the different turbine array sizes shows the importance of vertical transport for large array configurations. Quadrant-hole analysis is employed to gain a better understanding of the vertical energy transport at the top of the VAWT arrays. The results show a striking similarity between the flows in the VAWT arrays and the adjustment region of canopies. Namely, an increase in ejections and sweeps and decrease in inward and outward interactions occur inside the turbine array. Ejections are the strongest contributor, which is in agreement with the literature on evolving and sparse canopy flows. The influence of the turbine array size on the power output of the downstream turbines is examined by comparing a streamwise row of four single turbines with square arrays of nine turbine pairs. The results suggest that a new boundary layer forms on top of the larger turbine arrays as the flow adjusts to the new roughness length. This increases the turbulent energy transport over the whole planform area of the turbine array. By contrast, for the four single turbines, the vertical energy transport due to turbulent fluctuations is only increased in the near wake of the turbines. These findings add to the knowledge of energy transport in turbine arrays and therefore the optimization of the turbine spacing in wind farms.

We develop and characterize a low-order model of the mean flow through an array of vertical-axis wind turbines (VAWTs), consisting of a uniform flow and pairs of potential sources and sinks to represent each VAWT. The source and sink in each pair are of unequal strength, thereby forming a “leaky Rankine body” (LRB). In contrast to a classical Rankine body, which forms closed streamlines around a bluff body in potential flow, the LRB streamlines have a qualitatively similar appearance to a separated bluff body wake; hence, the LRB concept is used presently to model the VAWT wake. The relative strengths of the source and sink are determined from first principles analysis of an actuator disk model of the VAWTs. The LRB model is compared with field measurements of various VAWT array configurations measured over a 3-yr campaign. It is found that the LRB model correctly predicts the ranking of array performances to within statistical certainty. Furthermore, by using the LRB model to predict the flow around two-turbine and three-turbine arrays, we show that there are two competing fluid dynamic mechanisms that contribute to the overall array performance: turbine blockage, which locally accelerates the flow; and turbine wake formation, which locally decelerates the flow as energy is extracted. A key advantage of the LRB model is that optimal turbine array configurations can be found with significantly less computational expense than higher fidelity numerical simulations of the flow and much more rapidly than in experiments.

Full-scale, 3D, time-dependent aerodynamics and fluid‐structure interaction (FSI) simulations of a Darrieus-type vertical-axis wind turbine (VAWT) are presented. A structural model of the Windspire VAWT (Windspire energy, http://www.windspireenergy.com/ )i s developed, which makes use of the recently proposed rotation-free Kirchhoff‐Love shell and beam/cable formulations. A moving-domain finite-element-based ALE-VMS (arbitrary Lagrangian‐Eulerian-variational-multiscale) formulation is employed for the aerodynamics in combination with the sliding-interface formulation to handle the VAWT mechanical components in relative motion. The sliding-interface formulation is augmented to handle nonstationary cylindrical sliding interfaces, which are needed for the FSI modeling of VAWTs. The computational results presented show good agreement with the field-test data. Additionally, several scenarios are considered to investigate the transient VAWT response and the issues related to self-starting. [DOI: 10.1115/1.4027466]

As a first step toward characterizing coherent structures within the atmospheric surface layer (ASL), measurements obtained via a large-scale particle tracking velocimetry (LS-PTV) system were validated against wind-measurement station data as well as canonical turbulent boundary layer studies. The LS-PTV system resolves three-dimensional, Lagrangian tracks over a 16 m^3 volume. Mean-velocity measurements, as well as vertical and shear Reynolds-stress measurements, generally agreed with wind-measurement station data and Reynolds-stress profiles referenced from literature. The probability distributions for streamwise, spanwise and vertical velocity-fluctuation components appear normally distributed about zero. Furthermore, the probability distributions for all three components of Lagrangian acceleration were exponential and followed the parametrization curve from LaPorta et al. (Lett Nat 409:1017–1019, 2001). Lastly, the vorticity probability distributions were exponential and symmetric about zero, which matches findings from Balint et al. (Fluid Mech 228:53–86, 1991). The vorticity intensity measured by the LS-PTV system was less than values from Priyadarshana et al. (Fluid Mech 570:307–346, 2007), which is attributed to the low spatial resolution. However, the average spacing of 0.5 m between tracer particles is deemed sufficient for the future characterization of vortical structures within the ASL.

An investigation into redistribution of vorticity for rapidly accelerating plates with varying kinematics and initial conditions has been performed. Both three-dimensional particle tracking velocimetry and direct force measurements were applied simultaneously. The effective velocity of the feeding shear layer has been identified as the appropriate characteristic velocity rather than the commonly used plunge or free stream velocity. Based on this new normalization for circulation, it has been demonstrated that the existence of initial boundary-layer vorticity on the plunging plate – at least in the near-midplane region – does not contribute to the eventual vortex formation process. In accordance with the literature, however, the tip vortex positioning relative to the plate surface has been identified as an important contributor in the overall force production, particularly once the plate acceleration has ceased.

An investigation into the interdependency between acceleration and vorticity fields for rapidly accelerating, AR=4 plates with varying kinematics and initial conditions has been performed. In addition, the vorticity redistribution and reorientation in the plate’s proximity has also been studied. The data was obtained simultaneously by means of a threedimensional particle tracking velocimetry (3D-PTV) system together with a six-component force sensor. The effective velocity of the feeding shear layer has been identified as the appropriate characteristic velocity rather than the more commonly-used plunge or freestream velocities. Based on these newly-normalized circulation histories, it has been demonstrated that the existence of initial boundary-layer vorticity on the plunging plate - at least in the near midplane region - does not contribute to the eventual vortex formation. The comparison of identical plate kinematics with and without a superimposed uniform freestream velocity revealed a close interdependency of vorticity and Lagrangian acceleration fields. Consequently, a separation and/or superposition of circulatory and non-circulatory effects leads to an oversimplified description of such separated flows. In accordance with literature, the tip vortex has been identified to be an important contributor in the overall force production. Tip-vortex strength as well as its relative positioning to the plate surface influences the instantaneous force. As such, the orientation of the tip vortex becomes the critical contributor to lift once the acceleration of the plate has ceased.

Increased power production is observed in downstream vertical-axis wind turbines (VAWTs) when positioned offset from the wake of upstream turbines. This effect is found to exist in both laboratory and field environments with pairs of co- and counter-rotating turbines, respectively. It is hypothesized that the observed production enhancement is due to flow acceleration adjacent to the upstream turbine due to bluff body blockage, which would increase the incident freestream velocity on appropriately positioned downstream turbines. A low-order model combining potential flow and actuator disk theory captures this effect. Additional laboratory and field experiments further validate the predictive capabilities of the model. Finally, an evolutionary algorithm reveals patterns in optimized VAWT arrays with various numbers of turbines. A “truss-shaped” array is identified as a promising configuration to optimize energy extraction in VAWT wind farms by maximizing the performance enhancement of downstream turbines.

The interaction between leading-edge-vortex and tip-vortex development on a low-aspect-ratio plate has been investigated and compared to a nominally two-dimensional rectangular flat plate. Simultaneous to force measurements, three-dimensional particle tracking velocimetry (3D-PTV) was used to characterize the instantaneous flow field on the suction side. An integration of the spanwise circulation distribution for the two-dimensional case indicates that the leading-edge-vortex formation process is correlated with the convective time and not with the instantaneous pitch angle. However, for the finite plate, it is found that the tip-vortex formation process is correlated with the instantaneous pitch angle instead. Since leading-edge vorticity is convected inboard by tip-vortex-induced spanwise velocity, leading-edge-vortex growth is found to be retarded in the tip region. Finally, with the aid of Lagrangian particle tracks, the leading-edge and tip vortices are found to grow distinct from one another, that is, no leading-edge vorticity is drawn into the tip vortex. However, the tip vortex is found to influence the leading-edge-vortex dynamics through inboard transport of leading-edge vorticity and is therefore responsible for vortex compression at the mid-span.

In preparation of simultaneous large-scale / small-scale 3D Particle Tracking Velocimetry (3D-PTV) experiments in a developing turbulent flow we performed two types of measurements separately: (i) the velocity and coarse-grained velocity derivatives were measured in a large observation volume with focus on the large-scale flow features and (ii) spatially resolved velocity derivatives were measured in a small observation volume with the goal to obtain small-scale quantities associated with vorticity and strain. In this contribution we demonstrate that the characteristic flow structures were captured and velocity derivatives were accessed with sufficient accuracy. The problem of measuring velocity derivatives both in the Lagrangian and Eulerian frame of reference is also addressed. Although comparable accuracies in both settings could be achieved with our method, only statistics obtained from the spatially resolved measurement were found to be practically the same in both settings.

To improve the understanding of spike-type stall inception of a transonic axial compressor, measurements of the unsteady static pressure in the rotor endwall region are analyzed. At design speed, a detailed experimental investigation of the unsteadiness of the pressure field at the rotor endwall at near stall condition shows a strong fluctuation of the tip clearance flow. Both vortex strength and -trajectory oscillate randomly. Analysis of the wall pressure time histories during stall inception suggests that spike-type disturbances of the flow field correlate with an upstream motion of one blade passages shock front. In addition, the evolution of a stall cell could be visualized by means of static wall-pressure contour plots.Copyright © 2006 by ASME

The following study proposes a two-dimensional large-scale particle tracking velocimetry (LS-PTV) system to characterize coherent wind structures. Seven minutes of LS-PTV data is collected via an apparatus that seeds fog-filled soap bubbles into the wind at a height of 6m from the ground. The LS-PTV data is compared to 20 minutes of data collected concurrently from a wind mast at the same site. The LS-PTV system recorded a mean streamwise velocity of 1.35m/s with a standard deviation of 0.23m/s at a mean height of 2.50m with a standard deviation of 0.7m, which agrees well with the velocity profile measured by the wind mast. Furthermore, the Reynolds stresses measured by the LS-PTV system are found to compare to those measured by the wind mast and by Klebanoff [1] for a canonical turbulent boundary layer. The current study assumes that the centre-of-curvature trajectories of the particle pathlines are representative of the trajectories followed by the spanwise vortices. As a proof-of-principle study, this work has been successful in accurately describing the vortex distribution very near to the ground. However, the trajectories followed by the centres-of- curvat.ure belonging to pathlines concurrently passing through the field-of-view were sporadic and uncorrelated.

We analyze the flow field within an array of 18 counter-rotating, vertical-axis wind turbines (VAWTs), with an emphasis on the fluxes of mean and turbulence kinetic energy. The turbine wakes and the recovery of the mean wind speed between the turbine rows are derived from measurements of the velocity field using a portable meteorological tower with seven, vertically-staggered, three-component ultrasonic anemometers. The data provide insight to the blockage effect of both the individual turbine pairs within the array and the turbine array as a whole. The horizontal and planform kinetic energy fluxes into the turbine array are analyzed, and various models for the roughness length of the turbine array are compared. A high planform kinetic energy flux is measured for the VAWT array, which facilitates rapid flow recovery in the wake region behind the turbine pairs. Flow velocities return to 95% of the upwind value within six rotor diameters downwind from each turbine pair. This is less than half the recovery distance behind a typical horizontal-axis wind turbine (HAWT). The observed high level of the planform kinetic energy flux is correlated with higher relative roughness lengths for the VAWT array as compared to HAWT farms. This result is especially relevant for large wind farms with horizontal dimensions comparable to the height of the atmospheric boundary layer. As shown in recent work and confirmed here, the planform kinetic energy flux can be the dominant source of energy in such large-scale wind farms.