An Analytical Model for the Effect of Vertical Wind Veer on Wind Turbine Wakes

In this study, an analytical wake model for predicting the mean velocity field downstream of a wind turbine under veering incoming wind is systematically derived and validated. The new model, which is an extended version of the one introduced by Bastankhah and Porté-Agel, is based upon the application of mass conservation and momentum theorem and considering a skewed Gaussian distribution for the wake velocity deficit. Particularly, using a skewed (instead of axisymmetric) Gaussian shape allows accounting for the lateral shear in the incoming wind induced by the Coriolis force. This analytical wake model requires only the wake expansion rate as an input parameter to predict the mean wake flow downstream. The performance of the proposed model is assessed using the large-eddy simulation (LES) data of a full-scale wind turbine wake under the stably stratified condition. The results show that the proposed model is capable of predicting the skewed structure of the wake downwind of the turbine, and its prediction for the wake velocity deficit is in good agreement with the high-fidelity simulation data.

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The evolution of strained turbulent plane wakes

Journal of Fluid Mechanics ◽

10.1017/s0022112002008686 ◽

2002 ◽

Vol 463 ◽

pp. 53-120 ◽

Cited By ~ 27

Author(s):

MICHAEL M. ROGERS

Keyword(s):

Wake Flow ◽

Strain Rates ◽

Mean Flow ◽

Mean Velocity ◽

Velocity Deficit ◽

Self Similar Solution ◽

Flow Evolution ◽

Self Similar ◽

The Mean ◽

Pseudo Spectral

Direct numerical simulations of ten turbulent time-evolving strained wakes have been generated using a pseudo-spectral numerical method. In all the simulations, the strain was applied to the same (previously generated) initial developed self-similar wake flow field. The cases include flows in which the wake is subjected to various orientations of the applied mean strain, including both plane and axisymmetric strain configurations. In addition, for one particular strain geometry, cases with differing strain rates were considered. Although classical self-similar analysis does yield a self-similar solution for strained wakes, this solution does not describe the observed flow evolution. Instead, the wake mean velocity profiles evolve according to a different ‘equilibrium similarity solution’, with the strained wake width being determined by the straining in the inhomogeneous cross-stream direction. Wakes that are compressed in this direction eventually exhibit constant widths, whereas wakes in cases with expansive cross-stream strain ultimately spread at the same rate as the distortion caused by the applied strain. The shape of the wake mean velocity deficit profile is nearly universal. Although the effect of the strain on the mean flow is pronounced and rapid, the response of the turbulence to the strain occurs more slowly. Changes in the turbulence intensity cannot keep pace with changes in the mean wake velocity deficit, even for relatively low strain rates.

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Wakes behind two-dimensional surface obstacles in turbulent boundary layers

Journal of Fluid Mechanics ◽

10.1017/s0022112074002539 ◽

1974 ◽

Vol 64 (3) ◽

pp. 529-564 ◽

Cited By ~ 107

Author(s):

J. Counihan ◽

J. C. R. Hunt ◽

P. S. Jackson

Keyword(s):

Boundary Layer ◽

Wind Tunnel ◽

Turbulent Boundary Layer ◽

The Body ◽

Wake Flow ◽

Two Dimensional ◽

Mean Velocity ◽

Velocity Deficit ◽

Wind Tunnel Measurements ◽

The Mean

By making simple assumptions, an analytical theory is deduced for the mean velocity behind a two-dimensional obstacle (of heighth) placed on a rigid plane over which flows a turbulent boundary layer (of thickness δ). It is assumed thath[Gt ] δ, and that the wake can be divided into three regions. The velocity deficit −uis greatest in the two regions in which the change in shear stress is important, a wall region (W) close to the wall and a mixing region (M) spreading from the top of the obstacle. Above these is the external region (E) in which the velocity field is an inviscid perturbation on the incident boundary-layer velocity, which is taken to have a power-law profileU(y) =U∞(y−y1)n/δn, wheren[Gt ] 1. In (M), assuming that an eddy viscosity (=KhU(h)) can be defined for the perturbed flow in terms of the incident boundary-layer flow and that the velocity is self-preserving, it is found thatu(x,y) has the form$\frac{u}{U(h)} = \frac{ C }{Kh^2U^2(h)} \frac{f(n)}{x/h},\;\;\;\; {\rm where}\;\;\;\; \eta = (y/h)/[Kx/h]^{1/(n+2)}$, and the constant which defines the strength of the wake is$C = \int^\infty_0 y^U(y)(u-u_E)dy$, whereu=uE(x, y) asy→ 0 in region (E).In region (W),u(y) is proportional to Iny.By considering a large control surface enclosing the obstacle it is shown that the constant of the wake flow is not simply related to the drag of the obstacle, but is equal to the sum of the couple on the obstacle and an integral of the pressure field on the surface near the body.New wind-tunnel measurements of mean and turbulent velocities and Reynolds stresses in the wake behind a two-dimensional rectangular block on a roughened surface are presented. The turbulent boundary layer is artificially developed by well-established methods (Counihan 1969) in such a way that δ = 8h. These measurements are compared with the theory, with other wind-tunnel measurements and also with full-scale measurements of the wind behind windbreaks.It is found that the theory describes the distribution of mean velocity reasonably well, in particular the (x/h)−1decay law is well confirmed. The theory gives the correct self-preserving form for the distribution of Reynolds stress and the maximum increase of the mean-square turbulent velocity is found to decay downstream approximately as$ (\frac{x}{h})^{- \frac{3}{2}} $in accordance with the theory. The theory also suggests that the velocity deficit is affected by the roughness of the terrain (as measured by the roughness lengthy0) in proportion to In (h/y0), and there seems to be some experimental support for this hypothesis.

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Wind tunnel experiments on wind turbine wakes in yaw: effects of inflow turbulence and shear

Wind Energy Science ◽

10.5194/wes-3-329-2018 ◽

2018 ◽

Vol 3 (1) ◽

pp. 329-343 ◽

Cited By ~ 18

Author(s):

Jan Bartl ◽

Franz Mühle ◽

Jannik Schottler ◽

Lars Sætran ◽

Joachim Peinke ◽

...

Keyword(s):

Wind Turbine ◽

Laser Doppler Anemometry ◽

Vortex Pair ◽

Wake Flow ◽

Turbulent Shear ◽

Mean Velocity ◽

Inflow Turbulence ◽

The Mean ◽

Inflow Conditions ◽

Wake Characteristics

Abstract. The wake characteristics behind a yawed model wind turbine exposed to different customized inflow conditions are investigated. Laser Doppler anemometry is used to measure the wake flow in two planes at x∕D = 3 and x∕D = 6, while the turbine yaw angle is varied from γ=-30∘ to 0∘ to +30∘. The objective is to assess the influence of grid-generated inflow turbulence and shear on the mean and turbulent flow components. The wake flow is observed to be asymmetric with respect to negative and positive yaw angles. A counter-rotating vortex pair is detected creating a kidney-shaped velocity deficit for all inflow conditions. Exposing the rotor to non-uniform highly turbulent shear inflow changes the mean and turbulent wake characteristics only insignificantly. At low inflow turbulence the curled wake shape and wake center deflection are more pronounced than at high inflow turbulence. For a yawed turbine the rotor-generated turbulence profiles peak in regions of strong mean velocity gradients, while the levels of peak turbulence decrease at approximately the same rate as the rotor thrust.

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Wind tunnel experiments on wind turbine wakes in yaw: Effects of inflow turbulence and shear

10.5194/wes-2017-59 ◽

2018 ◽

Cited By ~ 1

Author(s):

Jan Bartl ◽

Franz Mühle ◽

Jannik Schottler ◽

Lars Sætran ◽

Joachim Peinke ◽

...

Keyword(s):

Wind Turbine ◽

Laser Doppler Anemometry ◽

Vortex Pair ◽

Wake Flow ◽

Mean Velocity ◽

Inflow Turbulence ◽

The Mean ◽

Center Deflection ◽

Inflow Conditions ◽

Wake Characteristics

Abstract. The wake characteristics behind a yawed model wind turbine exposed to different customized inflow conditions are investigated. Laser Doppler Anemometry is used to measure the wake flow in two planes at x/D = 3 and x/D = 6 while the turbine yaw angle is varied from −30° and 0° to +30°. The objective is to assess the influence of grid-generated inflow turbulence and shear on the mean and turbulent flow components. The wake flow is observed to be asymmetric with respect to negative and positive yaw angles. A counter-rotating vortex pair is detected creating a kidney-shaped velocity deficit for all inflow conditions. Exposing the rotor to non-uniform shear inflow changes the mean and turbulent wake characteristics only insignificantly. At low inflow turbulence the curled wake shape and wake center deflection are more pronounced than at high inflow turbulence. For a yawed turbine the rotor-generated turbulence profiles peak in regions of strong mean velocity gradients, while the levels of peak turbulence decrease at approximately the same rate as the rotor thrust.

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A Novel Analytical Wake Model with a Cosine-Shaped Velocity Deficit

Energies ◽

10.3390/en13133353 ◽

2020 ◽

Vol 13 (13) ◽

pp. 3353

Author(s):

Ziyu Zhang ◽

Peng Huang ◽

Haocheng Sun

Keyword(s):

Wind Turbine ◽

Numerical Data ◽

Streamwise Velocity ◽

Momentum Conservation ◽

Velocity Deficit ◽

Proposed Model ◽

Roughness Lengths ◽

Wake Model ◽

Aerodynamic Roughness ◽

Ambient Turbulence

A novel analytical model is proposed and validated in this paper to predict the velocity deficit in the wake downwind of a wind turbine. The model is derived by employing mass and momentum conservation and assuming a cosine-shaped distribution for the velocity deficit. In this model, a modified wake growth rate rather than a constant one is chosen to take into account the effects of the ambient turbulence and the mechanical turbulence generated. The model was tested against field observations, wind-tunnel measurements in different thrust operations and high-resolution large-eddy simulations (LES) for two aerodynamic roughness lengths. It was found that the normalized velocity deficit predicted by the proposed model shows good agreement with experimental and numerical data in terms of shape and magnitude in the far wake region ( x / d 0 > 3 ). Based on the proposed model, predictions from multiple views and at different locations are demonstrated to show the spatial distribution of streamwise velocity downwind of a wind turbine. The result shows that the model is suitable for predicting streamwise velocity fields and thus could provide some references for the selection of wind turbine spacing.

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Using the SWEPT Methodology for a Preliminary Wind Potential Estimation

ISRN Renewable Energy ◽

10.1155/2014/516964 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

Jean-Luc Menet

Keyword(s):

Wind Turbine ◽

Characteristic Curve ◽

Rayleigh Distribution ◽

Mean Velocity ◽

Technical Data ◽

Wind Potential ◽

Order Of Magnitude ◽

General Data ◽

The Mean ◽

A Site

The implantation of wind turbines generally follows a wind potential study which is made using specific numerical tools; the generated expenses are only acceptable for great projects. The purpose of the present paper is to propose a simplified methodology for the evaluation of the wind potential, following three successive steps for the determination of (i) the mean velocity, either directly or by the use of the most occurrence velocity (MOV); (ii) the velocity distribution coming from the single knowledge of the mean velocity by the use of a Rayleigh distribution and a Davenport-Harris law; (iii) an appropriate approximation of the characteristic curve of the turbine, coming from only two technical data. These last two steps allow calculating directly the electric delivered energy for the considered wind turbine. This methodology, called the SWEPT approach, can be easily implemented in a single worksheet. The results returned by the SWEPT tool are of the same order of magnitude than those given by the classical commercial tools. Moreover, everybody, even a “neophyte,” can use this methodology to obtain a first estimation of the wind potential of a site considering a given wind turbine, on the basis of very few general data.

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Blind test comparison of the performance and wake flow between two in-line wind turbines exposed to different atmospheric inflow conditions

10.5194/wes-2016-31 ◽

2016 ◽

Cited By ~ 1

Author(s):

Jan Bartl ◽

Lars Sætran

Keyword(s):

Wind Tunnel ◽

Wind Turbines ◽

Turbulence Intensity ◽

Wake Flow ◽

Detached Eddy Simulation ◽

Mean Velocity ◽

Blind Test ◽

The Mean ◽

Inlet Conditions ◽

Inflow Conditions

Abstract. This is a summary of the results of the fourth Blind test workshop which was held in Trondheim in October 2015. Herein, computational predictions on the performance of two in-line model wind turbines as well as the mean and turbulent wake flow are compared to experimental data measured at NTNU's wind tunnel. A detailed description of the model geometry, the wind tunnel boundary conditions and the test case specifications was published before the workshop. Expert groups within Computational Fluid Dynamics (CFD) were invited to submit predictions on wind turbine performance and wake flow without knowing the experimental results at the outset. The focus of this blind test comparison is to examine the model turbines' performance and wake development up until 9 rotor diameters downstream at three different atmospheric inflow conditions. Besides a spatially uniform inflow field of very low turbulence intensity (TI = 0.23 %) as well as high turbulence intensity (TI = 10.0 %), the turbines are exposed to a grid-generated atmospheric shear flow (TI = 10.1 %). Five different research groups contributed with their predictions using a variety of simulation models, ranging from fully resolved Reynolds Averaged Navier Stokes (RANS) models to Large Eddy Simulations (LES). For the three inlet conditions the power and the thrust force of the upstream turbine is predicted fairly well by most models, while the predictions of the downstream turbine's performance show a significantly higher scatter. Comparing the mean velocity profiles in the wake, most models approximate the mean velocity deficit level sufficiently well. However, larger variations between the models for higher downstream positions are observed. The prediction of the turbulence kinetic energy in the wake is observed to be very challenging. Both the LES model and the IDDES (Improved Delayed Detached Eddy Simulation) model, however, are consistently managing to provide fairly accurate predictions of the wake turbulence.

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Effect of wind turbine nacelle on turbine wake dynamics in large wind farms

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.206 ◽

2019 ◽

Vol 869 ◽

pp. 1-26 ◽

Cited By ~ 7

Author(s):

Daniel Foti ◽

Xiaolei Yang ◽

Lian Shen ◽

Fotis Sotiropoulos

Keyword(s):

Wind Turbine ◽

Coherent Structures ◽

Large Scale ◽

Wind Farm ◽

Wind Farms ◽

Practical Significance ◽

Mean Velocity ◽

Velocity Deficit ◽

Farm Scale ◽

Turbine Wake

Wake meandering, a phenomenon of large-scale lateral oscillation of the wake, has significant effects on the velocity deficit and turbulence intensities in wind turbine wakes. Previous studies of a single turbine (Kang et al., J. Fluid. Mech., vol. 774, 2014, pp. 374–403; Foti et al., Phys. Rev. Fluids, vol. 1 (4), 2016, 044407) have shown that the turbine nacelle induces large-scale coherent structures in the near field that can have a significant effect on wake meandering. However, whether nacelle-induced coherent structures at the turbine scale impact the emergent turbine wake dynamics at the wind farm scale is still an open question of both fundamental and practical significance. We take on this question by carrying out large-eddy simulation of atmospheric turbulent flow over the Horns Rev wind farm using actuator surface parameterisations of the turbines without and with the turbine nacelle taken into account. While the computed mean turbine power output and the mean velocity field away from the nacelle wake are similar for both cases, considerable differences are found in the turbine power fluctuations and turbulence intensities. Furthermore, wake meandering amplitude and area defined by wake meanders, which indicates the turbine wake unsteadiness, are larger for the simulations with the turbine nacelle. The wake influenced area computed from the velocity deficit profiles, which describes the spanwise extent of the turbine wakes, and the spanwise growth rate, on the other hand, are smaller for some rows in the simulation with the nacelle model. Our work shows that incorporating the nacelle model in wind farm scale simulations is critical for accurate predictions of quantities that affect the wind farm levelised cost of energy, such as the dynamics of wake meandering and the dynamic loads on downwind turbines.

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Aerodynamic Characteristics of Horizontal Axis Wind Turbine With Archimedes Spiral Blade

Volume 7B: Fluids Engineering Systems and Technologies ◽

10.1115/imece2013-62734 ◽

2013 ◽

Author(s):

Kyung Chun Kim ◽

Yoon Kee Kim ◽

Ho Seong Ji ◽

Jook Ho Beak ◽

Rinus Mieremet

Keyword(s):

Steady State ◽

Wind Turbine ◽

Cfd Simulation ◽

Aerodynamic Characteristics ◽

Wake Flow ◽

Power Coefficient ◽

Horizontal Axis Wind Turbine ◽

Mean Velocity ◽

Archimedes Spiral ◽

Spiral Blade

To investigate the aerodynamic characteristics of an Archimedes spiral wind turbine for urban-usage, both experimental and numerical studies were carried out. The Archimedes spiral blade was designed to produce wind power using drag and lift forces on the blade together. Instantaneous velocity fields were measured by two-dimensional PIV method in the near field of the blade. Mean velocity profiles were compared to those predicted by the steady state and unsteady state CFD simulation. It was found that the interaction between the wake flow at the rotor downstream and the induced velocity due to the tip vortices were strongly affected by the wind speed and resulting rotational speed of the blade. PIV measurements revealed the presence of dominant vertical structures at downstream the hub and near the blade tip. Unsteady CFD simulation results agreed well with those of PIV experiments than the steady state analysis. The power coefficient (Cp) obtained by CFD simulation demonstrated that the new type of wind turbine produced about 0.25, relatively high value compared to other types of urban-usage wind turbine.

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