Laboratory experiments were performed on a geometrically scaled verticalaxis wind turbine model over an unprecedented range of Reynolds numbers, including and exceeding those of the fullscale turbine. The study was performed in the highpressure 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 fullscale 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.
Stochastic theory and direct numerical simulations of the relative motion of highinertia particle pairs in isotropic turbulence
The relative velocities and positions of monodisperse highinertia 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 twotime correlation of fluid relative velocities seen by pairs that are nearly stationary. The twotime 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 largescale 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 integralscale 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. more »
 Award ID(s):
 1435953
 Publication Date:
 NSFPAR ID:
 10025836
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 813
 Page Range or eLocationID:
 205 to 249
 ISSN:
 00221120
 Sponsoring Org:
 National Science Foundation
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