skip to main content

Title: Vertical-axis wind turbine experiments at full dynamic similarity
Laboratory experiments were performed on a geometrically scaled vertical-axis wind turbine model over an unprecedented range of Reynolds numbers, including and exceeding those of the full-scale turbine. The study was performed in the high-pressure environment of the Princeton High Reynolds number Test Facility (HRTF). Utilizing highly compressed air as the working fluid enabled extremely high Reynolds numbers while still maintaining dynamic similarity by matching the tip speed ratio (defined as the ratio of tip velocity to free stream, $\unicode[STIX]{x1D706}=\unicode[STIX]{x1D714}R/U$ ) and Mach number (defined at the turbine tip, $Ma=\unicode[STIX]{x1D714}R/a$ ). Preliminary comparisons are made with measurements from the full-scale field turbine. Peak power for both the field data and experiments resides around $\unicode[STIX]{x1D706}=1$ . In addition, a systematic investigation of trends with Reynolds number was performed in the laboratory, which revealed details about the asymptotic behaviour. It was shown that the parameter that characterizes invariance in the power coefficient was the Reynolds number based on blade chord conditions ( $Re_{c}$ ). The power coefficient reaches its asymptotic value when $Re_{c}>1.5\times 10^{6}$ , which is higher than what the field turbine experiences. The asymptotic power curve is found, which is invariant to further increases in Reynolds number.
; ; ; ; ;
Award ID(s):
Publication Date:
Journal Name:
Journal of Fluid Mechanics
Page Range or eLocation-ID:
707 to 720
Sponsoring Org:
National Science Foundation
More Like this
  1. The relative velocities and positions of monodisperse high-inertia particle pairs in isotropic turbulence are studied using direct numerical simulations (DNS), as well as Langevin simulations (LS) based on a probability density function (PDF) kinetic model for pair relative motion. In a prior study (Rani et al. , J. Fluid Mech. , vol. 756, 2014, pp. 870–902), the authors developed a stochastic theory that involved deriving closures in the limit of high Stokes number for the diffusivity tensor in the PDF equation for monodisperse particle pairs. The diffusivity contained the time integral of the Eulerian two-time correlation of fluid relative velocities seenmore »by pairs that are nearly stationary. The two-time correlation was analytically resolved through the approximation that the temporal change in the fluid relative velocities seen by a pair occurs principally due to the advection of smaller eddies past the pair by large-scale eddies. Accordingly, two diffusivity expressions were obtained based on whether the pair centre of mass remained fixed during flow time scales, or moved in response to integral-scale eddies. In the current study, a quantitative analysis of the (Rani et al. 2014) stochastic theory is performed through a comparison of the pair statistics obtained using LS with those from DNS. LS consist of evolving the Langevin equations for pair separation and relative velocity, which is statistically equivalent to solving the classical Fokker–Planck form of the pair PDF equation. Langevin simulations of particle-pair dispersion were performed using three closure forms of the diffusivity – i.e. the one containing the time integral of the Eulerian two-time correlation of the seen fluid relative velocities and the two analytical diffusivity expressions. In the first closure form, the two-time correlation was computed using DNS of forced isotropic turbulence laden with stationary particles. The two analytical closure forms have the advantage that they can be evaluated using a model for the turbulence energy spectrum that closely matched the DNS spectrum. The three diffusivities are analysed to quantify the effects of the approximations made in deriving them. Pair relative-motion statistics obtained from the three sets of Langevin simulations are compared with the results from the DNS of (moving) particle-laden forced isotropic turbulence for $St_{\unicode[STIX]{x1D702}}=10,20,40,80$ and $Re_{\unicode[STIX]{x1D706}}=76,131$ . Here, $St_{\unicode[STIX]{x1D702}}$ is the particle Stokes number based on the Kolmogorov time scale and $Re_{\unicode[STIX]{x1D706}}$  is the Taylor micro-scale Reynolds number. Statistics such as the radial distribution function (RDF), the variance and kurtosis of particle-pair relative velocities and the particle collision kernel were computed using both Langevin and DNS runs, and compared. The RDFs from the stochastic runs were in good agreement with those from the DNS. Also computed were the PDFs $\unicode[STIX]{x1D6FA}(U|r)$ and $\unicode[STIX]{x1D6FA}(U_{r}|r)$ of relative velocity $U$ and of the radial component of relative velocity $U_{r}$ respectively, both PDFs conditioned on separation $r$ . The first closure form, involving the Eulerian two-time correlation of fluid relative velocities, showed the best agreement with the DNS results for the PDFs.« less
  2. We mimic a flapping wing through a fluid–structure interaction (FSI) framework based upon a generalized lumped-torsional flexibility model. The developed fluid and structural solvers together determine the aerodynamic forces, wing deformation and self-propelled motion. A phenomenological solution to the linear single-spring structural dynamics equation is established to help offer insight and validate the computations under the limit of small deformation. The cruising velocity and power requirements are evaluated by varying the flapping Reynolds number ( $20\leqslant Re_{f}\leqslant 100$ ), stiffness (represented by frequency ratio, $1\lesssim \unicode[STIX]{x1D714}^{\ast }\leqslant 10$ ) and the ratio of aerodynamic to structural inertia forces (represented bymore »a dimensionless parameter $\unicode[STIX]{x1D713}$ ( $0.1\leqslant \unicode[STIX]{x1D713}\leqslant 3$ )). For structural inertia dominated flows ( $\unicode[STIX]{x1D713}\ll 1$ ), pitching and plunging are shown to always remain in phase ( $\unicode[STIX]{x1D719}\approx 0$ ) with the maximum wing deformation occurring at the end of the stroke. When aerodynamics dominates ( $\unicode[STIX]{x1D713}>1$ ), a large phase difference is induced ( $\unicode[STIX]{x1D719}\approx \unicode[STIX]{x03C0}/2$ ) and the maximum deformation occurs at mid-stroke. Lattice Boltzmann simulations show that there is an optimal $\unicode[STIX]{x1D714}^{\ast }$ at which cruising velocity is maximized and the location of optimum shifts away from unit frequency ratio ( $\unicode[STIX]{x1D714}^{\ast }=1$ ) as $\unicode[STIX]{x1D713}$ increases. Furthermore, aerodynamics administered deformations exhibit better performance than those governed by structural inertia, quantified in terms of distance travelled per unit work input. Closer examination reveals that although maximum thrust transpires at unit frequency ratio, it is not transformed into the highest cruising velocity. Rather, the maximum velocity occurs at the condition when the relative tip displacement ${\approx}\,0.3$ .« less
  3. To design and optimize arrays of vertical-axis wind turbines (VAWTs) for maximal power density and minimal wake losses, a careful consideration of the inherently three-dimensional structure of the wakes of these turbines in real operating conditions is needed. Accordingly, a new volumetric particle-tracking velocimetry method was developed to measure three-dimensional flow fields around full-scale VAWTs in field conditions. Experiments were conducted at the Field Laboratory for Optimized Wind Energy (FLOWE) in Lancaster, CA, using six cameras and artificial snow as tracer particles. Velocity and vorticity measurements were obtained for a 2 kW turbine with five straight blades and a 1more »kW turbine with three helical blades, each at two distinct tip-speed ratios and at Reynolds numbers based on the rotor diameter $D$ between $1.26 \times 10^{6}$ and $1.81 \times 10^{6}$ . A tilted wake was observed to be induced by the helical-bladed turbine. By considering the dynamics of vortex lines shed from the rotating blades, the tilted wake was connected to the geometry of the helical blades. Furthermore, the effects of the tilted wake on a streamwise horseshoe vortex induced by the rotation of the turbine were quantified. Lastly, the implications of this dynamics for the recovery of the wake were examined. This study thus establishes a fluid-mechanical connection between the geometric features of a VAWT and the salient three-dimensional flow characteristics of its near-wake region, which can potentially inform both the design of turbines and the arrangement of turbines into highly efficient arrays.« less
  4. Lifting line theory describes the cumulative effect of shed vorticity from finite span lifting surfaces. In this work, the theory is reformulated to improve the accuracy of the actuator line model (ALM). This model is a computational tool used to represent lifting surfaces, such as wind-turbine blades in computational fluid dynamics. In ALM, blade segments are represented by means of a Gaussian body force distribution with a prescribed kernel size. Prior analysis has shown that a representation of the blade using an optimal kernel width $\unicode[STIX]{x1D716}^{opt}$ of approximately one quarter of the chord size results in accurate predictions of themore »velocity field and loads along the blades. Also, simulations have shown that use of the optimal kernel size yields accurate representation of the tip-vortex size and the associated downwash resulting in accurate predictions of the tip losses. In this work, we address the issue of how to represent the effects of finite span wings and tip vortices when using Gaussian body forces with a kernel size larger than the optimal value. This question is relevant in the context of coarse-scale large-eddy simulations that cannot afford the fine resolutions required to resolve the optimal kernel size. For this purpose, we present a filtered lifting line theory for a Gaussian force distribution. Based on the streamwise component of the vorticity transport equation, we develop an analytical model for the induced velocity resulting from the spanwise changes in lift force for an arbitrary kernel scale. The results are used to derive a subfilter-scale velocity model that is used to correct the velocity along the blade when using kernel sizes larger than $\unicode[STIX]{x1D716}^{opt}$ . Tests are performed in large-eddy simulation of flow over fixed wings with constant and elliptic chord distributions using various kernel sizes. Results show that by using the proposed subfilter velocity model, kernel-size independent predictions of lift coefficient and total lift forces agree with those obtained with the optimal kernel size.« less
  5. Direct numerical simulations of turbulent boundary layers with a nominal free-stream Mach number of $6$ and a Reynolds number of $Re_{\unicode[STIX]{x1D70F}}\approx 450$ are conducted at a wall-to-recovery temperature ratio of $T_{w}/T_{r}=0.25$ and compared with a previous database for $T_{w}/T_{r}=0.76$ in order to investigate pressure fluctuations and their dependence on wall temperature. The wall-temperature dependence of widely used velocity and temperature scaling laws for high-speed turbulent boundary layers is consistent with previous studies. The near-wall pressure-fluctuation intensities are dramatically modified by wall-temperature conditions. At different wall temperatures, the variation of pressure-fluctuation intensities as a function of wall-normal distance is dramatically modifiedmore »in the near-wall region but remains almost intact away from the wall. Wall cooling also has a strong effect on the frequency spectrum of wall-pressure fluctuations, resulting in a higher dominant frequency and a sharper spectrum peak with a faster roll-off at both the high- and low-frequency ends. The effect of wall cooling on the free-stream noise spectrum can be largely accounted for by the associated changes in boundary-layer velocity and length scales. The pressure structures within the boundary layer and in the free stream evolve less rapidly as the wall temperature decreases, resulting in an increase in the decorrelation length of coherent pressure structures for the colder-wall case. The pressure structures propagate with similar speeds for both wall temperatures. Due to wall cooling, the generated pressure disturbances undergo less refraction before they are radiated to the free stream, resulting in a slightly steeper radiation wave front in the free stream. Acoustic sources are largely concentrated in the near-wall region; wall cooling most significantly influences the nonlinear (slow) component of the acoustic source term by enhancing dilatational fluctuations in the viscous sublayer while damping vortical fluctuations in the buffer and log layers.« less