arXiv subjects

Nathaniel J. Wei

Publications and source records attributed to Nathaniel J. Wei.

9 recordsLinked to original sources

arXiv2026

Time-varying wind-turbine wakes at high Reynolds numbers

Wind turbines operating in the atmospheric boundary layer are constantly exposed to time-varying flow conditions. These disturbances often occur on similar time scales to wind-turbine controllers, which may interfere with wind-farm control strategies that operate under steady-flow assumptions. This study aims to investigate the significance of such time variations on wind-turbine wake dynamics, focusing on slow time scales representative of quasi-steady processes in large wind farms. Experiments are conducted at near utility-scale Reynolds numbers ($Re_D=4\times10^6$) in a pressurized-air wind tunnel, with a wind turbine forced in periodic rotation-rate oscillations by means of a time-varying generator torque at low Strouhal numbers ($St=0.04$). Flow measurements in the wake of the turbine demonstrate that disturbances propagate through the wake as traveling waves, which are advected nonlinearly at the velocity of the wake rather than that of the free stream. The wake behavior can be described in a quasi-steady manner, but only after wake advection is accounted for by a Lagrangian transformation. Even in the quasi-steady regime, the spatiotemporal evolution of the wake can be controlled by independently varying the turbine thrust and tip-speed ratio. The results suggest that wake advection is important to consider for wind-farm modeling and control, and that time-varying control may allow wind-turbine wake interactions to be tuned even in nominally quasi-steady conditions for optimal wind-farm performance.

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arXiv2024

Wake dynamics of wind turbines in unsteady streamwise flow conditions

The unsteady flow physics of wind-turbine wakes under dynamic forcing conditions are critical to the modeling and control of wind farms for optimal power density. Unsteady forcing in the streamwise direction may be generated by unsteady inflow conditions in the atmospheric boundary layer, dynamic induction control of the turbine, or streamwise surge motions of a floating offshore wind turbine due to floating-platform oscillations. This study seeks to identify the dominant flow mechanisms in unsteady wakes forced by a periodic upstream inflow condition. A theoretical framework for the problem is derived, which describes traveling-wave undulations in the wake radius and streamwise velocity. These dynamics encourage the aggregation of tip vortices into large structures that are advected along in the wake. Flow measurements in the wake of a periodically surging turbine were obtained in an optically accessible towing-tank facility, with an average diameter-based Reynolds number of 300,000 and with surge-velocity amplitudes of up to 40% of the mean inflow velocity. Qualitative agreement between trends in the measurements and model predictions is observed, supporting the validity of the theoretical analyses. The experiments also demonstrate large enhancements in the recovery of the wake relative to the steady-flow case, with wake-length reductions of up to 46.5% and improvements in the available power at 10 diameters downstream of up to 15.7%. These results provide fundamental insights into the dynamics of unsteady wakes and serve as additional evidence that unsteady fluid mechanics can be leveraged to increase the power density of wind farms.

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arXiv2024

Modeling unsteady loads on wind-turbine blade sections from periodic structural oscillations and impinging gusts

Many traditional methods for wind turbine design and analysis assume quasi-steady aerodynamics, but atmospheric flows are inherently unsteady and modern turbine blades are susceptible to aeroelastic deformations. This study therefore evaluates the effectiveness of simple analytical models for capturing the effects of such unsteady conditions on wind-turbine blades. We consider a pitching and plunging airfoil in a periodic transverse gust as an idealization of unsteady loading scenarios on a blade section. A potential-flow model derived from a linear combination of canonical problems is proposed to predict the unsteady lift on a two-dimensional airfoil in the small-perturbation limit. We then perform high-fidelity two-dimensional numerical simulations of a NACA-0012 airfoil over a range of periodic pitch, plunge, and gust disturbances, and quantify the amplitude and phase of the unsteady lift response. Good agreement with the model predictions is found for low to moderate forcing amplitudes and frequencies, while deviations are observed when the angle-of-attack amplitudes approach the static flow-separation limit of the airfoil. Potential explanations are given for the cases in which the ideal-flow theory proves insufficient. This theoretical framework and numerical evaluation motivate the inclusion of unsteady flow models in design and simulation tools in order to increase the robustness and operational lifespans of wind turbine blades in real flow conditions.

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arXiv2023

Power-generation enhancements and upstream flow properties of turbines in unsteady inflow conditions

Energy-harvesting systems in complex flow environments, such as floating offshore wind turbines, tidal turbines, and ground-fixed turbines in axial gusts, encounter unsteady streamwise flow conditions that affect their power generation and structural loads. In some cases, enhancements in time-averaged power generation above the steady-flow operating point are observed. To characterize these dynamics, a nonlinear dynamical model for the rotation rate and power extraction of a periodically surging turbine is derived and connected to two potential-flow representations of the induction zone upstream of the turbine. The model predictions for the time-averaged power extraction of the turbine and the upstream flow velocity and pressure are compared against data from experiments conducted with a surging-turbine apparatus in an open-circuit wind tunnel at a diameter-based Reynolds number of $Re_D = 6.3\times10^5$ and surge-velocity amplitudes of up to 24% of the wind speed. The combined modeling approach captures trends in both the time-averaged power extraction and the fluctuations in upstream flow quantities, while relying only on data from steady-flow measurements. The sensitivity of the observed increases in time-averaged power to steady-flow turbine characteristics is established, thus clarifying the conditions under which these enhancements are possible. Finally, the influence of unsteady fluid mechanics on time-averaged power extraction is explored analytically. The theoretical framework and experimental validation provide a cohesive modeling approach that can drive the design, control, and optimization of turbines in unsteady flow conditions, as well as inform the development of novel energy-harvesting systems that can leverage unsteady flows for large increases in power-generation capacities.

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arXiv2021

Phase-Averaged Dynamics of a Periodically Surging Wind Turbine

The unsteady power generation of a wind turbine translating in the streamwise direction is relevant to floating offshore wind turbines, kite-mounted airborne wind turbines, and other non-traditional wind-energy systems. To study this problem experimentally, measurements of torque, rotor speed, and power were acquired for a horizontal-axis wind turbine actuated in periodic surge motions in a fan-array wind tunnel at the Caltech Center for Autonomous Systems and Technologies (CAST). Experiments were conducted at a diameter-based Reynolds number of $Re_D=6.1\times10^5$ and at tip-speed ratios between 5.2 and 8.8. Sinusoidal and trapezoidal surge-velocity waveforms with maximum surge velocities up to 23% of the free-stream velocity were tested. A model in the form of a linear ordinary differential equation (first-order in time) was derived to capture the time-resolved dynamics of the surging turbine. Its coefficients were obtained using torque measurements from a stationary turbine, without the need for unsteady calibrations. Its predictions compared favorably with the measured amplitude- and phase-response data. Furthermore, increases in the period-averaged power of up to 6.4% above the steady reference case were observed in the experiments at high tip-speed ratios and surge velocities, potentially due to unsteady or nonlinear aerodynamic effects. Conversely, decreases in mean power with increased surge velocity at low tip-speed ratios were likely a result of the onset of stall on the turbine blades. These results inform the development of strategies to optimize and control the unsteady power generation of periodically surging wind turbines, and motivate further investigations into the unsteady aerodynamics of wind-energy systems.

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arXiv2020

Near-wake structure of full-scale vertical-axis wind turbines

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 1-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 these 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.

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arXiv2019

Sinusoidal-gust generation with a pitching and plunging airfoil

The generation of uniform, periodic gust disturbances in an experimental context is demonstrated using a single oscillating airfoil. A pitching and heaving symmetric airfoil is suggested as a simpler alternative to existing gust-generation methods. The Theodorsen theory of unsteady aerodynamics is used as an analytical tool to dictate the kinematics necessary to produce well-defined sinusoidal gusts downstream of the airfoil. These analytic predictions improve the symmetry of fluctuations in the vertical velocity induced by the airfoil, as well as minimize the influence of vorticity shed by the oscillating airfoil. The apparatus is shown to produce smooth, repeatable gusts with high amplitudes and reduced frequencies compared to other gust-generation mechanisms in the literature. Furthermore, the control of downstream flow properties by airfoil motion kinematics has applications in experimental aerodynamics, the design of rotorcraft and light aerial vehicles, and biological propulsion.

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arXiv2019

Control of long-range correlations in turbulence

The character of turbulence depends on where it develops. Turbulence near boundaries, for instance, is different than in a free stream. To elucidate the differences between flows, it is instructive to vary the structure of turbulence systematically, but there are few ways of stirring turbulence that make this possible. In other words, an experiment typically examines either a boundary layer or a free stream, say, and the structure of the turbulence is fixed by the geometry of the experiment. We introduce a new active grid with many more degrees of freedom than previous active grids. The additional degrees of freedom make it possible to control various properties of the turbulence. We show how long-range correlations in the turbulent velocity fluctuations can be shaped by changing the way the active grid moves. Specifically, we show how not only the correlation length but also the detailed shape of the correlation function depends on the correlations imposed in the motions of the grid. Until now, large-scale structure had not been adjustable in experiments. This new capability makes possible new systematic investigations into turbulence dissipation and dispersion, for example, and perhaps in flows that mimic features of boundary layers, free streams, and flows of intermediate character.

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arXiv2018

Insights into the Periodic Gust Response of Airfoils

The unsteady lift response of an airfoil in a sinusoidal gust can be modeled by two transfer functions: the first-order Sears function and the second-order Atassi function, albeit leading to different results under certain conditions. Previous studies have shown that the Sears function holds in experiments, but recently Cordes et al. (2017) reported experimental data that corresponded to the Atassi function rather than the Sears function. In order to clarify the observed discrepancy, the specific differences between these models are isolated analytically in this study and are related to physical gust parameters. Gusts with these parameters are then produced in wind-tunnel experiments using an active-grid gust generator. Measurements of the unsteady gust loads on an airfoil in the wind tunnel at Reynolds numbers ($Re_c$) of $2.0\times 10^5$ and $2.6\times 10^5$ and reduced frequencies between 0.09 and 0.42 confirm that the decisive difference between the Sears and Atassi functions lies in the character of the gust and not in the characteristics of the airfoil. The differences in the gust-response data between Sears and Atassi gust conditions are shown to be significant only at low reduced frequencies. These findings are supported by numerical simulations of the experimental setup. Finally, the influence of boundary-layer turbulence on experimental convergence with model predictions is investigated. These results serve to clarify the conditions under which the Sears and Atassi functions can be applied, and they establish the validity of both in an experimental context.

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