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

2012 ◽  
Vol 4 (6) ◽  
pp. 063105 ◽  
Author(s):  
Nicholas Hamilton ◽  
Hyung Suk Kang ◽  
Charles Meneveau ◽  
Raúl Bayoán Cal
Keyword(s):  
Boundary Layer ◽  
Statistical Analysis ◽  
Kinetic Energy ◽  
Wind Turbine

Prediction of laminar, transitional and turbulent flow regimes, based on three-equation k-ω turbulence model

2008 ◽  
Vol 112 (1134) ◽  
pp. 469-476 ◽  
Author(s):  
R. Taghavi-Zenouz ◽  
M. Salari ◽  
M. Etemadi
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Wind Turbine ◽  
Flat Plate ◽  
Turbine Blade ◽  
Wind Turbine Blade ◽  
Freestream Turbulence ◽  
Boundary Layer Flows ◽  
Laminar Separation ◽  
Transitional Boundary Layer

Abstract A recently developed transitional model for boundary-layer flows has been examined on a flat plate and the well-known S809 wind turbine blade. Proposed numerical model tries to simulate streamwise fluctuations, induced by freestream turbulence, in pre-transitional boundary-layer flows by introducing an additional transport equation for laminar kinetic energy term. This new approach can be used for modeling of transitional flows which are exposed to both the freestream turbulence intensity and streamwise pressure gradient, which are known as the most dominant factors in occurrence of transition. Computational method of this model is based on the solution of the Reynolds averaged Navier-Stokes (RANS) equations and the eddy-viscosity concept. The model includes three transport equations of laminar kinetic energy, turbulent kinetic energy and dissipation rate frequency. The present model is capable of predicting either natural or bypass transitional mechanisms, which may occur in attached boundary-layer flows. In addition, the model can simulate transition in the separated free shear layers and the subsequent turbulent re-attachment to form a laminar separation bubble. Flat plate was exposed to different freestream turbulence intensities and streamwise pressure gradients. Wind turbine blade was examined under two different Reynolds numbers, with one of them suitable for the occurrence of laminar separation bubbles on its surfaces. To evaluate the performance of this new model in resolving transitional boundary-layer flows, final results have been compared to those obtained through application of conventional turbulence models. Comparison of final results for the flat plate and the S809 aerofoil with available experimental data show very close agreements.

scholarly journals The problem of the second wind turbine – a note on a common but flawed wind power estimation method

2012 ◽  
Vol 3 (1) ◽  
pp. 79-86 ◽  
Author(s):  
F. Gans ◽  
L. M. Miller ◽  
A. Kleidon
Keyword(s):  
Boundary Layer ◽  
Simple Model ◽  
Kinetic Energy ◽  
Atmospheric Boundary Layer ◽  
Wind Turbine ◽  
Wind Power ◽  
Momentum Conservation ◽  
Height Velocity ◽  
Power Extraction ◽  
Order Of Magnitude

Abstract. Several recent wind power estimates suggest that this renewable energy resource can meet all of the current and future global energy demand with little impact on the atmosphere. These estimates are calculated using observed wind speeds in combination with specifications of wind turbine size and density to quantify the extractable wind power. However, this approach neglects the effects of momentum extraction by the turbines on the atmospheric flow that would have effects outside the turbine wake. Here we show with a simple momentum balance model of the atmospheric boundary layer that this common methodology to derive wind power potentials requires unrealistically high increases in the generation of kinetic energy by the atmosphere. This increase by an order of magnitude is needed to ensure momentum conservation in the atmospheric boundary layer. In the context of this simple model, we then compare the effect of three different assumptions regarding the boundary conditions at the top of the boundary layer, with prescribed hub height velocity, momentum transport, or kinetic energy transfer into the boundary layer. We then use simulations with an atmospheric general circulation model that explicitly simulate generation of kinetic energy with momentum conservation. These simulations show that the assumption of prescribed momentum import into the atmospheric boundary layer yields the most realistic behavior of the simple model, while the assumption of prescribed hub height velocity can clearly be disregarded. We also show that the assumptions yield similar estimates for extracted wind power when less than 10% of the kinetic energy flux in the boundary layer is extracted by the turbines. We conclude that the common method significantly overestimates wind power potentials by an order of magnitude in the limit of high wind power extraction. Ultimately, environmental constraints set the upper limit on wind power potential at larger scales rather than detailed engineering specifications of wind turbine design and placement.

scholarly journals Assessing spacing impact on coherent features in a wind turbine array boundary layer

2018 ◽  
Vol 3 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Naseem Ali ◽  
Nicholas Hamilton ◽  
Dominic DeLucia ◽  
Raúl Bayoán Cal
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Flow ◽  
Wind Turbine ◽  
Reynolds Stress ◽  
Energy Content ◽  
Turbulence Kinetic Energy ◽  
Flow Structures ◽  
Spanwise Direction ◽  
The Impact

Abstract. As wind farms become larger, the spacing between turbines becomes a significant design consideration that can impose serious economic constraints. To investigate the turbulent flow structures in a 4 × 3 Cartesian wind turbine array boundary layer (WTABL), a wind tunnel experiment was carried out parameterizing the streamwise and spanwise wind turbine spacing. Four cases are chosen spacing turbines by 6 or 3D in the streamwise direction, and 3 or 1.5D in the spanwise direction, where D = 12 cm is the rotor diameter. Data are obtained experimentally using stereo particle image velocimetry. Mean streamwise velocity showed maximum values upstream of the turbine with the spacing of 6 and 3D in the streamwise and spanwise direction, respectively. Fixing the spanwise turbine spacing to 3D, variations in the streamwise spacing influence the turbulent flow structure and the power available to following wind turbines. Quantitative comparisons are made through spatial averaging, shifting measurement data and interpolating to account for the full range between devices to obtain data independent of array spacing. The largest averaged Reynolds stress is seen in cases with spacing of 3D × 3D. Snapshot proper orthogonal decomposition (POD) was employed to identify the flow structures based on the turbulence kinetic energy content. The maximum turbulence kinetic energy content in the first POD mode is seen for turbine spacing of 6D × 1.5D. The flow upstream of each wind turbine converges faster than the flow downstream according to accumulation of turbulence kinetic energy by POD modes, regardless of spacing. The streamwise-averaged profile of the Reynolds stress is reconstructed using a specific number of modes for each case; the case of 6D × 1.5D spacing shows the fastest reconstruction to compare the rate of reconstruction of statistical profiles. Intermediate modes are also used to reconstruct the averaged profile and show that the intermediate scales are responsible for features seen in the original profile. The variation in streamwise and spanwise spacing leads to changes in the background structure of the turbulence, where the color map based on barycentric map and Reynolds stress anisotropy tensor provides an alternate perspective on the nature of the perturbations within the wind turbine array. The impact of the streamwise and spanwise spacings on power produced is quantified, where the maximum production corresponds with the case of greatest turbine spacing.

scholarly journals Wind Turbine Performance in Very Large Wind Farms: Betz Analysis Revisited

Energies ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1078 ◽  
Author(s):  
Jacob R. West ◽  
Sanjiva K. Lele
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Wind Turbine ◽  
Wind Farm ◽  
Wind Farms ◽  
Mean Flow ◽  
Thrust Coefficient ◽  
Turbine Performance ◽  
Trade Offs ◽  
Mean Kinetic Energy

The theoretical limit for wind turbine performance, the so-called Betz limit, arises from an inviscid, irrotational analysis of the streamtube around an actuator disk. In a wind farm in the atmospheric boundary layer, the physics are considerably more complex, encompassing shear, turbulent transport, and wakes from other turbines. In this study, the mean flow streamtube around a wind turbine in a wind farm is investigated with large eddy simulations of a periodic array of actuator disks in half-channel flow at a range of turbine thrust coefficients. Momentum and mean kinetic energy budgets are presented, connecting the energy budget for an individual turbine to the wind farm performance as a whole. It is noted that boundary layer turbulence plays a key role in wake recovery and energy conversion when considering the entire wind farm. The wind farm power coefficient is maximized when the work done by Reynolds stress on the periphery of the streamtube is maximized, although some mean kinetic energy is also dissipated into turbulence. This results in an optimal value of thrust coefficient lower than the traditional Betz result. The simulation results are used to evaluate Nishino’s model of infinite wind farms, and design trade-offs described by it are presented.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

scholarly journals Large-Eddy Simulation of Wind Turbine Flows: A New Evaluation of Actuator Disk Models

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3745
Author(s):  
Tristan Revaz ◽  
Fernando Porté-Agel
Keyword(s):  
Boundary Layer ◽  
Simple Model ◽  
Wind Turbine ◽  
Wake Flow ◽  
Test Case ◽  
Flow Solver ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Layer Flow ◽  
Advanced Model

Large-eddy simulation (LES) with actuator models has become the state-of-the-art numerical tool to study the complex interaction between the atmospheric boundary layer (ABL) and wind turbines. In this paper, a new evaluation of actuator disk models (ADMs) for LES of wind turbine flows is presented. Several details of the implementation of such models are evaluated based on a test case studied experimentally. In contrast to other test cases used in previous similar studies, the present test case consists of a wind turbine immersed in a realistic turbulent boundary-layer flow, for which accurate data for the turbine, the flow, the thrust and the power are available. It is found that the projection of the forces generated by the turbine into the flow solver grid is crucial for rotor predictions, especially for the power, and less important for the wake flow prediction. In this context, the projection of the forces into the flow solver grid should be as accurate as possible, in order to conserve the consistency between the computed axial velocity and the projected axial force. Also, the projection of the force is found to be much more important in the rotor plane directions than in the streamwise direction. It is found that for the case of a wind turbine immersed in a realistic turbulent boundary-layer flow, the potential spurious numerical oscillations originating from sharp force projections are not harmful to the results. By comparing an advanced model which computes the non-uniform distribution of the turbine forces over the rotor with a simple model which assumes uniform effects of the turbine forces, it is found that both can lead to accurate results for the far wake flow and the thrust and power predictions. However, the comparison shows that the advanced model leads to better results for the near wake flow. In addition, it is found that the simple model overestimates the rotor velocity prediction in comparison to the advanced model. These elements are explained by the lack of local feedback between the axial velocity and the axial force in the simple model. By comparing simulations with and without including the effects of the nacelle and tower, it is found that the consideration of the nacelle and tower is relatively important both for the near wake and the power prediction, due to the shadow effects. The grid resolution is not found to be critical once a reasonable resolution is used, i.e. in the order of 10 grid points along each direction across the rotor. The comparison with the experimental data shows that an accurate prediction of the flow, thrust, and power is possible with a very reasonable computational cost. Overall, the results give important guidelines for the implementation of ADMs for LES.

scholarly journals Spatiotemporal Dynamics of the Kinetic Energy in the Atmospheric Boundary Layer from Minisodar Measurements

Atmosphere ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 421
Author(s):  
Alexander Potekaev ◽  
Liudmila Shamanaeva ◽  
Valentina Kulagina
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Atmospheric Boundary Layer ◽  
Turbulent Kinetic Energy ◽  
Time Of Day ◽  
Linear Increase ◽  
Spatiotemporal Dynamics ◽  
Intermediate Layers ◽  
Subsequent Decrease ◽  
Stable Atmospheric Boundary Layer

Spatiotemporal dynamics of the atmospheric kinetic energy and its components caused by the ordered and turbulent motions of air masses are estimated from minisodar measurements of three velocity vector components and their variances within the lowest 5–200 m layer of the atmosphere, with a particular emphasis on the turbulent kinetic energy. The layered structure of the total atmospheric kinetic energy has been established. From the diurnal hourly dynamics of the altitude profiles of the turbulent kinetic energy (TKE) retrieved from minisodar data, four layers are established by the character of the altitude TKE dependence, namely, the near-ground layer, the surface layer, the layer with a linear TKE increase, and the transitive layer above. In the first layer, the most significant changes of the TKE were observed in the evening hours. In the second layer, no significant changes in the TKE values were observed. A linear increase in the TKE values with altitude was observed in the third layer. In the fourth layer, the TKE slightly increased with altitude and exhibited variations during the entire observation period. The altitudes of the upper boundaries of these layers depended on the time of day. The MKE values were much less than the corresponding TKE values, they did not exceed 50 m2/s2. From two to four MKE layers were distinguished based on the character of its altitude dependence. The two-layer structures were observed in the evening and at night (under conditions of the stable atmospheric boundary layer). In the morning and daytime, the four-layer MKE structures with intermediate layers of linear increase and subsequent decrease in the MKE values were observed. Our estimates demonstrated that the TKE contribution to the total atmospheric kinetic energy considerably (by a factor of 2.5–3) exceeded the corresponding MKE contribution.

Analysis of an Airfoil Using a Transition and Turbulence Model

2016 ◽  
Vol 819 ◽  
pp. 356-360
Author(s):  
Mazharul Islam ◽  
Jiří Fürst ◽  
David Wood ◽  
Farid Nasir Ani
Keyword(s):  
Fluid Dynamics ◽  
Boundary Layer ◽  
Computational Fluid Dynamics ◽  
Kinetic Energy ◽  
Turbulence Model ◽  
Original Version ◽  
Transitional Region ◽  
Cfd Analysis ◽  
Computational Fluid Dynamics Cfd

In order to evaluate the performance of airfoils with computational fluid dynamics (CFD) tools, modelling of transitional region in the boundary layer is very critical. Currently, there are several classes of transition-based turbulence model which are based on different methods. Among these, the k-kL- ω, which is a three equation turbulence model, is one of the prominent ones which is based on the concept of laminar kinetic energy. This model is phenomenological and has several advantageous features. Over the years, different researchers have attempted to modify the original version which was proposed by Walter and Cokljat in 2008 to enrich the modelling capability. In this article, a modified form of k-kL-ω transitional turbulence model has been used with the help of OpenFOAM for an investigative CFD analysis of a NACA 4-digit airfoil at range of angles of attack.

Utilisation of kinetic energy from wind turbine for grid connections: a review paper

2018 ◽  
Vol 12 (6) ◽  
pp. 615-624 ◽  
Author(s):  
Dongxiao Wang ◽  
Xiaodan Gao ◽  
Ke Meng ◽  
Jing Qiu ◽  
Loi Lei Lai ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Wind Turbine ◽  
Review Paper
Sign in / Sign up

Export Citation Format

Share Document