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

Hamilton, Nicholas; Kang, Hyung Suk; Meneveau, Charles; Cal, Raúl Bayoán

doi:10.1063/1.4761921

Cited by 82 publications

(68 citation statements)

References 43 publications

(26 reference statements)

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“…As expected from other wind tunnel studies for wind energy [36][37][38], positive values of −uv occur above hub height in the wake. This component of the Reynolds shear stresses is associated with the vertical flux of mean flow kinetic energy by turbulence and remediation of the wake.…”

Section: A Turbulence Fieldsupporting

confidence: 55%

“…Figure 2 shows the selected planes as bold dashed lines in the wake of the fourth row of wind turbines. Sample data correspond to measurements at x/D = 0.5, reflecting the near wake where the intermittency is greatest [35], and x/D = 6 in the far wake, where the momentum deficit in the wake has largely recovered and the flow is well-mixed [36]. Turbulence statistics at x/D = 6 represents the flow that would be seen by successive rows of devices.…”

Section: A Wind Turbine Wake: Experimental Datamentioning

confidence: 99%

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Anisotropic character of low-order turbulent flow descriptions through the proper orthogonal decomposition

2017

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Proper orthogonal decomposition (POD) is applied to distinct data sets in order to characterize the propagation of error arising from basis truncation in the description of turbulence. Experimental data from stereo particle image velocimetry measurements in a wind turbine array and direct numerical simulation data from a fully developed channel flow are used to illustrate dependence of the anisotropy tensor invariants as a function of POD modes used in low-order descriptions. In all cases, ensembles of snapshots illuminate a variety of anisotropic states of turbulence. In the near wake of a model wind turbine, the turbulence field reflects the periodic interaction between the incoming flow and rotor blade. The far wake of the wind turbine is more homogenous, confirmed by the increased magnitude of the anisotropy factor. By contrast, the channel flow exhibits many anisotropic states of turbulence. In the inner layer of the wall-bounded region, one observes onecomponent turbulence at the wall; immediately above, the turbulence is dominated by two components, with the outer layer showing fully three-dimensional turbulence, conforming to theory for wall-bounded turbulence. The complexity of flow descriptions resulting from truncated POD bases can be greatly mitigated by severe basis truncations. However, the current work demonstrates that such simplification necessarily exaggerates the anisotropy of the modeled flow and, in extreme cases, can lead to the loss of three-dimensionality. Application of simple corrections to the low-order descriptions of the Reynolds stress tensor significantly reduces the residual root-mean-square error. Similar error reduction is seen in the anisotropy tensor invariants. Corrections of this form reintroduce three-dimensionality to severe truncations of POD bases. A threshold for truncating the POD basis based on the equivalent anisotropy factor for each measurement set required many more modes than a threshold based on energy. The mode requirement to reach the anisotropy threshold after correction is reduced by a full order of magnitude for all example data sets, ensuring that economical low-dimensional models account for the isotropic quality of the turbulence field.

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Section: A Turbulence Fieldsupporting

confidence: 55%

Section: A Wind Turbine Wake: Experimental Datamentioning

confidence: 99%

Anisotropic character of low-order turbulent flow descriptions through the proper orthogonal decomposition

2017

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“…Numerical simulations of flow over large wind farms have suggested that the rate of TKE exchange with less turbulent and faster-moving air aloft determines how the wake region decays (Calaf et al 2010). Wind-tunnel investigations (Hamilton et al 2012) suggest a coupling between the dissipation rate, small-scale turbulence, and the large-scale structures of the flow in the upper portions of the wake.…”

Section: Introductionmentioning

confidence: 99%

Dissipation of Turbulence in the Wake of a Wind Turbine

Lundquist

Bariteau

2014

Boundary-Layer Meteorol

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The wake of a wind turbine is characterized by increased turbulence and decreased wind speed. Turbines are generally deployed in large groups in wind farms, and so the behaviour of an individual wake as it merges with other wakes and propagates downwind is critical in assessing wind-farm power production. This evolution depends on the rate of turbulence dissipation in the wind-turbine wake, which has not been previously quantified in field-scale measurements. In situ measurements of winds and turbulence dissipation from the wake region of a multi-MW turbine were collected using a tethered lifting system (TLS) carrying a payload of high-rate turbulence probes. Ambient flow measurements were provided from sonic anemometers on a meteorological tower located near the turbine. Good agreement between the tower measurements and the TLS measurements was established for a case without a wind-turbine wake. When an operating wind turbine is located between the tower and the TLS so that the wake propagates to the TLS, the TLS measures dissipation rates one to two orders of magnitude higher in the wake than outside of the wake. These data, collected between two and three rotor diameters D downwind of the turbine, document the significant enhancement of turbulent kinetic energy dissipation rate within the wind-turbine wake. These wake measurements suggest that it may be useful to pursue modelling approaches that account for enhanced dissipation. Comparisons of wake and non-wake dissipation rates to mean wind speed, wind-speed variance, and turbulence intensity are presented to facilitate the inclusion of these measurements in wake modelling schemes.

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“…Results are compared in the wake of the WT and of the AD. The transport equation of the mean-flow kinetic-energy (2) is obtained as by Hamilton et al (2012), with a Reynolds double decomposition of the flow where u i is the time average velocity in the i-direction and K E is the mean-flow average kinetic energy, p is the pressure, and u 0 i u 0 j are the Reynolds stresses. The third term of the right-hand-side of Eq.…”

Section: F Theorymentioning

confidence: 99%

Experimental comparison of a wind-turbine and of an actuator-disc near wake

Lignarolo

Ragni

Ferreira

et al. 2016

Journal of Renewable and Sustainable Energy

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The actuator disc (AD) model is commonly used to simplify the simulation of horizontal-axis wind-turbine aerodynamics. The limitations of this approach in reproducing the wake losses in wind farm simulations have been proven by a previous research. The present study is aimed at providing an experimental analysis of the near-wake turbulent flow of a wind turbine (WT) and a porous disc, emulating the actuator disc numerical model. The general purpose is to highlight the similarities and to quantify the differences of the two models in the near-wake region, characterised by the largest discrepancies. The velocity fields in the wake of a wind turbine model and a porous disc (emulation of the actuator disc numerical model) have been measured in a wind tunnel using stereo particle image velocimetry. The study has been conducted at low turbulence intensity in order to separate the problems of the flow mixing caused by the external turbulence and the one caused by the turbulence induced directly by the AD or the WT presence. The analysis, as such, showed the intrinsic differences and similarities between the flows in the two wakes, solely due to the wake-induced flow, with no influence of external flow fluctuations. The data analysis provided the time-average three-component velocity and turbulence intensity fields, pressure fields, rotor and disc loading, vorticity fields, stagnation enthalpy distribution, and mean-flow kinetic-energy fluxes in the shear layer at the border of the wake. The properties have been compared in the wakes of the two models. Even in the absence of turbulence, the results show a good match in the thrust and energy coefficient, velocity, pressure, and enthalpy fields between wind turbine and actuator disc. However, the results show a different turbulence intensity and turbulent mixing. The results suggest the possibility to extend the use of the actuator disc model in numerical simulation until the very near wake, provided that the turbulent mixing is correctly represented.

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

Cited by 82 publications

References 43 publications

Anisotropic character of low-order turbulent flow descriptions through the proper orthogonal decomposition

Anisotropic character of low-order turbulent flow descriptions through the proper orthogonal decomposition

Dissipation of Turbulence in the Wake of a Wind Turbine

Experimental comparison of a wind-turbine and of an actuator-disc near wake

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