Nicholas Hamilton

Statistical analysis of kinetic energy entrainment in a model wind turbine array boundary layer

For large wind farms, kinetic energy must be entrained from the flow above the wind turbines to replenish wakes and enable power extraction in the array. Various statistical features of turbulence causing vertical entrainment of mean-flow kinetic energy are studied using hot-wire velocimetry data taken in a model wind farm in a scaled wind tunnel experiment. Conditional statistics and spectral decompositions are employed to characterize the most relevant turbulent flow structures and determine their length-scales. Sweep and ejection events are shown to be the largest contributors to the vertical kinetic energy flux, although their relative contribution depends upon the location in the wake. Sweeps are shown to be dominant in the region above the wind turbine array. A spectral analysis of the data shows that large scales of the flow, about the size of the rotor diameter in length or larger, dominate the vertical entrainment. The flow is less incoherent below the array, causing decreased vertical fluxes the...

Low-order representations of the canonical wind turbine array boundary layer via double proper orthogonal decomposition

Wind turbine wakes are investigated in order to characterize the development of energetic turbulence structures. Experimental data from stereo particle image velocimetry render the full Reynolds stress tensor accessible in planes parallel to the swept area of the scale model turbine rotor. Proper orthogonal decomposition (POD) is applied to decompose and analyze structures in the wake. The modes resulting from the decomposition demonstrate that structures grow and develop along the streamwise direction. A second iteration of the snapshot POD, otherwise called double proper orthogonal decomposition (DPOD), is applied to modes of common rank from the span of measurement locations yielding an ordered set of projections. The DPOD describes the sub-modal organization in terms of largest common projection and a series of correction modes with coefficients that are functions of the streamwise coordinate. Sub-structures of POD modes that persist through the wake have a dominant projection that accounts for the ch...

Anisotropy of the Reynolds stress tensor in the wakes of wind turbine arrays in Cartesian arrangements with counter-rotating rotors

A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear stress −vw¯. The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds stress anisotropy tensor (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate s...

Anisotropy stress invariants of thermally stratified wind turbine array boundary layers using large eddy simulations

In the interest of understanding the dynamics and energy transfer between the atmospheric boundary layer and large wind turbine arrays, a description of the turbulence anisotropy in the wake region of wind turbines is necessary. Flux of high momentum flow into the wind turbine array by anisotropic turbulence is a dominant factor of mean kinetic energy resupply for the wind farm. Under thermal stratification, the behavior of the turbulence field, and the energy flux, is significantly altered. Here, a thermally stratified wind turbine array boundary layer is studied in detail using a combination of Lumley and barycentric maps together with the recently introduced spheroid and color maps. The atmospheric flow is modelled using a large eddy simulation driven by a constant geostrophic wind and a time-varying ground surface temperature, obtained from a selected period of the Cooperative Atmosphere-Surface Exchange Study-99 field experiment. The wind farm is modelled using the traditional actuator-disk with rota...

Low-order dynamical system model of a fully developed turbulent channel flow

A reduced order model of a turbulent channel flow is composed from a direct numerical simulation database hosted at the Johns Hopkins University. Snapshot proper orthogonal decomposition (POD) is used to identify the Hilbert space from which the reduced order model is obtained, as the POD basis is defined to capture the optimal energy content by mode. The reduced order model is defined by coupling the evolution of the dynamic POD mode coefficients through their respective time derivative with a least-squares polynomial fit of terms up to third order. Parameters coupling the dynamics of the POD basis are defined in analog to those produced in the classical Galerkin projection. The resulting low-order dynamical system is tested for a range of basis modes demonstrating that the non-linear mode interactions do not lead to a monotonic decrease in error propagation. A basis of five POD modes accounts for 50% of the integrated turbulence kinetic energy but captures only the largest features of the turbulence in ...

Turbulent and Deterministic Stresses in the Near Wake of a Wind Turbine Array

A wind tunnel experiment was conducted to investigate the evolution of the stress field in the wake of a wind turbine array boundary layer. Phase-locked stereo particle image velocimetry measurements were taken in planes parallel to the turbine rotor and progressing throughout the near wake. Turbulent stresses vary significantly as a function of phase angle of the turbine rotor blades in the near wake. The resupply of kinetic energy to the momentum-deficit area of the wake is accomplished largely through the flux term in the mean kinetic energy equation. Phase-dependent contributions to the total flux into the wake indicate that turbulent structures impart periodic increases in entrainment of high-momentum flow. Deviations of phase-averaged velocities from total mean values are used to formulate deterministic stresses, which provide relatively decreased overall contributions to the flux of kinetic energy into the wake. Contributions of deterministic stresses are redudeced in the wake due to turbulent mixing in the wind turbine canopy. Based on the observable dependence of the Reynolds stresses on the phase orientation of the rotor blades, decomposition analogous to that of the deterministic stresses is applied directly to the Reynolds stress tensor. Termed the tertiary decomposition, root-mean-square deviations of the phase-averaged from the time-averaged turbulent stress tensor, and associated contributions to the flux of kinetic energy are shown to be of the same order of magnitude as the turbulence and greater than deterministic contributions.

Experimental Study of Turbine Hub Height Variation on Wind Farms

Characteristics of a wind turbine array boundary layer under controlled variations of the hub height of the turbines are studied through wind tunnel experiments. The atmosphere has been reproduced using a passive grid, strakes and roughness elements. Particle image velocimetry technique is employed to obtain converged statistics at four locations at the centerline. The array consists of a four by three arrangement. The velocity eld is then studied, mean velocity and uctuations, to observe dierences attributed to the change in hub height of the turbine.