Entrainment Of Kinetic Energy Research Articles

How incoming turbulence affects wake recovery of an NREL-5MW wind turbine

The present work aims at investigating the effect of inflow turbulence on the wake recovery of the NREL-5MW reference wind turbine. The wake produced by a utility-scale wind turbine invested by both a laminar uniform inflow and a turbulent flow, is analyzed by means of proper-orthogonal decomposition (POD). The considered turbine is the NREL-5MW at tip-speed ratio λ = 7 and a diameter-based Reynolds number of the order 108. The flow is simulated through Large Eddy Simulation, where the forces exerted by the blades are modeled using the Actuator Line Method, whereas tower and nacelle are modeled employing the immersed boundary method. The main flow structures identified by modal decomposition in both of the considered cases are compared, and some differences emerge, which can be of great importance for the formulation of a reduced-order model. Among the most energetic modes, a high-frequency mode directly related to the tip vortices is found only in the flow case with laminar inflow. In the presence of inflow turbulence, the most energetic modes are all composed by large-scale low-frequency structures filling the whole domain. We evaluate the contribution of each POD mode to wake recovery reconstructing the total flux of mean kinetic energy due to turbulent fluctuations on a closed surface enclosing the wake of the wind turbine. In the laminar-inflow case, we have found that the POD modes related to the tip and root vortices do not contribute positively to the wake recovery, but they rather sustains the velocity gradient, as already established by Lignarolo et al. (2015) for a wind-turbine model. Whereas, in the turbulent-inflow case, all the most energetic modes contribute positively to wake recovery. These results clearly indicate that inflow turbulence should be taken into account for accurately estimate the entrainment process in the wake of wind turbines.NREL 5MW wind turbine, POD, laminar or turbulent inflow, wake recovery, turbulent kinetic energy entrainment.

The effect of coastal terrain on nearshore offshore wind farms: A large-eddy simulation study

Performance of offshore wind farms built in the nearshore region will be affected by onshore terrain with higher turbulence in the flow when wind is blowing from land toward sea. Current study employs large-eddy simulation to investigate the effect of coastal terrain on the performance of large nearshore offshore wind farms. At first, two atmospheric boundary layer (ABL) simulation cases are defined to investigate the evolution of an internal boundary layer (IBL) during the sea-to-land and land-to-sea transition of the flow. The growth rate of the IBL was similar for both ABL simulation cases. However, the mean velocity-based definition of IBL heights, which essentially are the equilibrium layer, were half the height of shear stress-based IBLs. The first wind farm simulation case only considers an offshore surface, while the second case includes the region with land-to-sea transition upstream of the wind farm. Better wake recovery is observed in the case that considers the effect of onshore terrain. This is attributed to the higher inflow turbulence level, which resulted in higher entrainment of kinetic energy from the flow above. The farm-induced IBL for a land-to-sea transition case shows rapid growth for the first few turbine rows, while the offshore only case shows gradual growth. However, the difference between the two IBLs decreases with downstream distance, implying that for sufficiently long wind farms, both IBLs will converge. Total power output of the land-to-sea transition case is 17% higher than the offshore only case for the farm layout and roughness heights considered in this study.

Blade planform design optimization to enhance turbine wake control

AbstractThis study considers optimizing the planform of wind turbine blades to ultimately enhance wind plant controls, namely, wake steering strategies. Adjoint‐enabled unsteady actuator line simulations are carried out to obtain gradients for optimization of several different performance objectives with respect to blade chord length at 10 locations along blade span. We demonstrate different blade design optimizations that can maximize time‐averaged lateral wake deflection, entrainment of kinetic energy, or total power of multiple turbines. Our optimized designs can produce a 4+% increase in wake deflection, a 4× increase in vertical kinetic energy entrainment, or a 3.6% increase in power when compared with the baseline case. While lateral wake deflection is only modestly sensitive to chord changes, we find that increasing the outboard chord length can dramatically increase kinetic energy entrainment, resulting in faster wake recovery and gains in net power. While this work develops only a few case studies emphasizing relative performance improvements and general trends, these results show the promise of a framework that combines mid‐fidelity computation with adjoint‐based optimization for control and design problems.

Effects of atmospheric stability on the performance of a wind turbine located behind a three-dimensional hill

Understanding the effect of thermal stratification on wind turbine wakes in complex terrain is essential to optimize wind farm design. The effect of a three-dimensional hill on the performance of a downwind turbine is studied by performing large eddy simulations for different atmospheric conditions. The distance between the hill and the turbine is six times the turbine diameter, and the hill height is equal to the hub height. It is shown that the hill wake reduces the power production of the downstream turbine by 35% for the convective boundary layer case under consideration. However, surprisingly, the wind turbine power production is increased by about 24% for the stable boundary layer case considered here. This phenomenon results from the entrainment of kinetic energy from the low-level jet due to the increased mixing induced by the hill wake. This effect strongly depends on the Coriolis force-induced wind veer. The increased turbulence intensity by the hill results in a strong increase in the forces experienced by the blades, which suggest the turbine is experiencing much higher unsteady turbulence loading. It is shown that the increase in the power fluctuations may not fully reflect the increase in the force fluctuations on the blades.

Big wind power: seven questions for turbulence research

ABSTRACTThe accelerating growth of wind energy in recent years mandates improved understanding of wind turbine, wind farm and atmospheric turbulence interactions. Fluid turbulence plays a vital role in these interactions, motivating the present formulation of several pertinent questions for turbulence research. These questions touch upon the need for better analytical, synthetic and reduced order models of turbulence, better model coupling methods and basic understanding of flow phenomena governing kinetic energy entrainment and limiting power densities. Responding to the formulated questions may lead to improvements in wind energy harvesting.

Quantification of Preferential Contribution of Reynolds Shear Stresses and Flux of Mean Kinetic Energy Via Conditional Sampling in a Wind Turbine Array

Conditional statistics are employed in analyzing wake recovery and Reynolds shear stress (RSS) and flux directional out of plane component preference. Examination of vertical kinetic energy entrainment through describing and quantifying the aforementioned quantities has implications on wind farm spacing, design, and power production, and also on detecting loading variation due to turbulence. Stereographic particle image velocimetry measurements of incoming and wake flow fields are taken for a 3 × 4 model wind turbine array in a scaled wind tunnel experiment. Reynolds shear stress component is influenced by ⟨uv⟩ component, whereas ⟨vw⟩ is more influenced by streamwise advection of the flow; u, v, and w being streamwise, vertical, and spanwise velocity fluctuations, respectively. Relative comparison between sweep and ejection events, ΔS⟨uiuj⟩, shows the role of streamwise advection of momentum on RSS values and direction. It also shows their tendency to an overall balanced distribution. ⟨uw⟩ intensities are associated with ejection elevated regions in the inflow, yet in the wake, ⟨uw⟩ is linked with sweep dominance regions. Downward momentum flux occupies the region between hub height and top tip. Sweep events contribution to downward momentum flux is marginally greater than ejection events'. When integrated over the swept area, sweeps contribute 55% of the net downward kinetic energy flux and 45% is the ejection events contribution. Sweep dominance is related to momentum deficit as its value in near wake elevates 30% compared to inflow. Understanding these quantities can lead to improved closure models.

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 rotation and yaw-alignment. The results show that turbulence under unstable stratification tends to be more isotropic than that under neutral and stable stratification. The turbulent mixing attributed to positive buoyancy in unstable regimes determines the energy distribution between flow layers, directly affecting the vertical distribution of anisotropy. Contrarily, in the stably stratified flow, negative buoyancy damps the turbulent fluctuations, hence affecting the evolution of the Reynolds stress, leading to an increase of flow anisotropy. In both thermal stratification regimes, wind turbines alter the structure of the turbulence within the atmospheric boundary layer by creating regions of greater anisotropy and expanding the boundary layer vertically. For the modeling community, it is important to note that the wind turbine wakes display a larger degree of anisotropy that is related well to the production of turbulent kinetic energy and mean kinetic energy entrainment, and hence, it is important to model correctly for accurate power forecasting. Leveraging the new insights into wind turbine/atmospheric boundary layer interaction found here will benefit the formulation of a new generation of efficient low order models for commercial application.

Numerical Investigation of Aerodynamic Performance and Loads of a Novel Dual Rotor Wind Turbine

The objective of this paper is to numerically investigate the effects of the atmospheric boundary layer on the aerodynamic performance and loads of a novel dual-rotor wind turbine (DRWT). Large eddy simulations are carried out with the turbines operating in the atmospheric boundary layer (ABL) and in a uniform inflow. Two stability conditions corresponding to neutral and slightly stable atmospheres are investigated. The turbines are modeled using the actuator line method where the rotor blades are modeled as body forces. Comparisons are drawn between the DRWT and a comparable conventional single-rotor wind turbine (SRWT) to assess changes in aerodynamic efficiency and loads, as well as wake mixing and momentum and kinetic energy entrainment into the turbine wake layer. The results show that the DRWT improves isolated turbine aerodynamic performance by about 5%–6%. The DRWT also enhances turbulent axial momentum entrainment by about 3.3 %. The highest entrainment is observed in the neutral stability case when the turbulence in the ABL is moderately high. Aerodynamic loads for the DRWT, measured as out-of-plane blade root bending moment, are marginally reduced. Spectral analyses of ABL cases show peaks in unsteady loads at the rotor passing frequency and its harmonics for both rotors of the DRWT.

Tip-vortex instability and turbulent mixing in wind-turbine wakes

Kinetic-energy transport and turbulence production within the shear layer of a horizontal-axis wind-turbine wake are investigated with respect to their influence on the tip-vortex pairwise instability, the so-called leapfrogging instability. The study quantifies the effect of near-wake instability and tip-vortex breakdown on the process of mean-flow kinetic-energy transport within the far wake of the wind turbine, in turn affecting the wake re-energising process. Experiments are conducted in an open-jet wind tunnel with a wind-turbine model of 60 cm diameter at a diameter-based Reynolds number range$\mathit{Re}_{D}=150\,000{-}230\,000$. The velocity fields in meridian planes encompassing a large portion of the wake past the rotor are measured both in the unconditioned and the phase-locked mode by means of stereoscopic particle image velocimetry. The detailed topology and development of the tip-vortex interactions are discussed prior to a statistical analysis based on the triple decomposition of the turbulent flow fields. The study emphasises the role of the pairing instability as a precursor to the onset of three-dimensional vortex distortion and breakdown, leading to increased turbulent mixing and kinetic-energy transport across the shear layer. Quadrant analysis further elucidates the role of sweep and ejection events within the two identified mixing regimes. Prior to the onset of the instability, vortices shed from the blade appear to inhibit turbulent mixing of the expanding wake. The second region is dominated by the leapfrogging instability, with a sudden increase of the net entrainment of kinetic energy. Downstream of the latter, random turbulent motion characterises the flow, with a significant increase of turbulent kinetic-energy production. In this scenario, the leapfrogging mechanism is recognised as the triggering event that accelerates the onset of efficient turbulent mixing followed by the beginning of the wake re-energising process.

Large eddy simulation of a large wind-turbine array in a conventionally neutral atmospheric boundary layer

Under conventionally neutral conditions, the boundary layer is frequently capped by an inversion layer, which counteracts vertical entrainment of kinetic energy. Very large wind farms are known to depend on vertical entrainment to transport energy from above the farm towards the turbines. In this study, large eddy simulations of an infinite wind-turbine array in a conventionally neutral atmospheric boundary layer are performed. By carefully selecting the initial potential-temperature profile, the influence of the height and the strength of a capping inversion on the power output of a wind farm is investigated. Results indicate that both the height and the strength have a significant effect on the boundary layer flow, and that the height of the neutral boundary layer is effectively controlled by the capping inversion. In addition, it is shown that the vertical entrainment rate decreases for increasing inversion strength or height. In our infinite wind-farm simulations, varying the inversion characteristics leads to differences in power extraction on the order of 13% ± 0.2% (for increasing the strength from 2.5 to 10 K), and 31% ± 0.4% (for increasing the height from 500 to 1500 m). A detailed analysis of the mean kinetic-energy equation is included, showing that the variation in power extraction originates from the work done by the driving pressure gradient related to the boundary layer height and the geostrophic angle, while entrainment of kinetic energy from the free atmosphere does not play a significant role. Also, the effect of inversion strength on power extraction is energetically not related to different amounts of energy entrained, but explained by a difference in boundary layer growth, leading to higher boundary layers for lower inversion strengths. We further present a simple analytical model that allows to obtain wind-farm power output and driving power for the fully developed regime as function of Rossby number and boundary layer height.

Kinetic energy entrainment in wind turbine and actuator disc wakes: an experimental analysis

The present experimental study focuses on the comparison between the wake of a two-bladed wind turbine and the one of an actuator disk. The flow field at the middle plane of the wake is measured with a stereoscopic particle image velocimetry setup, in the low-speed Open Jet Facility wind tunnel of the Delft University of Technology. The wind turbine wake is characterized by the complex dynamics of the tip vortex development and breakdown. Analysis of the flow statistics show anisotropic turbulent fluctuations in the turbine wake, with stronger components in the radial direction. The wake of the actuator disc is instead characterized by isotropic random fluctuations. The mixing process in the shear layer is further analysed in terms of flux of mean flow kinetic energy, to show the main differences between the kinetic energy entrainment in the actuator and the turbine wake. This project is intended to provide the basis for understanding the origin of the limitations of the current wake models based on the actuator disc assumption.

Mean and turbulent kinetic energy budgets inside and above very large wind farms under conventionally-neutral condition

In this study, large-eddy simulations (LES) is combined with a turbine model to investigate all the terms in the budgets of mean and turbulent kinetic energy (TKE) inside and above very large wind farms. Emphasis is placed on quantifying the relative contribution of the thermal stratification in the free-atmosphere and wind-turbine spacing on the energy balance. The mean kinetic energy budget through the wind farms indicates that the magnitude of the kinetic energy entrainment form the free atmosphere into the boundary layer increases by increasing the density of the farms and decreasing the static stability in the free atmosphere, leading to larger power output from the wind farms. This entrainment is the only source of kinetic energy to balance that extracted by the turbines inside very large wind farms. In addition, it is shown that the distribution of the kinetic energy flux above the wind turbines, at top-tip level, is quite heterogeneous and its magnitude just behind the wind turbines is much larger due to the strong wind shear at that level. The simulation results also show that increasing the wind-farm density leads to an increase in the boundary-layer height, the ratio of the ageostrophic to the geostrophic velocity component inside the boundary layer, and the potential temperature near the surface. Detailed analysis of the TKE budget through the wind farms reveals also an important effect of the thermal stratification and wind turbine spacing on the magnitude and spatial distribution of the shear production, dissipation rate and transport terms. In particular, the shear production and dissipation rate have a peak at the turbine-top level, where the wind shear is largest, and their magnitude increases as the static stability in the free atmosphere and the wind-turbine spacing decrease.

Experimental Study on Influence of Pitch Motion on the Wake of a Floating Wind Turbine Model

Wind tunnel experiments were performed, where the development of the wake of a model wind turbine was measured using stereo Particle Image Velocimetry to observe the influence of platform pitch motion. The wakes of a classical bottom fixed turbine and a streamwise oscillating turbine are compared. Results indicate that platform pitch creates an upward shift in all components of the flow and their fluctuations. The vertical flow created by the pitch motion as well as the reduced entrainment of kinetic energy from undisturbed flows above the turbine result in potentially higher loads and less available kinetic energy for a downwind turbine. Experimental results are compared with four wake models. The wake models employed are consistent with experimental results in describing the shapes and magnitudes of the streamwise velocity component of the wake for a fixed turbine. Inconsistencies between the model predictions and experimental results arise in the floating case particularly regarding the vertical displacement of the velocity components of the flow. Furthermore, it is found that the additional degrees of freedom of a floating wind turbine add to the complexity of the wake aerodynamics and improved wake models are needed, considering vertical flows and displacements due to pitch motion.

Large eddy simulation study of the kinetic energy entrainment by energetic turbulent flow structures in large wind farms

In this study, we address the question of how kinetic energy is entrained into large wind turbine arrays and, in particular, how large-scale flow structures contribute to such entrainment. Previous research has shown this entrainment to be an important limiting factor in the performance of very large arrays where the flow becomes fully developed and there is a balance between the forcing of the atmospheric boundary layer and the resistance of the wind turbines. Given the high Reynolds numbers and domain sizes on the order of kilometers, we rely on wall-modeled large eddy simulation (LES) to simulate turbulent flow within the wind farm. Three-dimensional proper orthogonal decomposition (POD) analysis is then used to identify the most energetic flow structures present in the LES data. We quantify the contribution of each POD mode to the kinetic energy entrainment and its dependence on the layout of the wind turbine array. The primary large-scale structures are found to be streamwise, counter-rotating vortices located above the height of the wind turbines. While the flow is periodic, the geometry is not invariant to all horizontal translations due to the presence of the wind turbines and thus POD modes need not be Fourier modes. Differences of the obtained modes with Fourier modes are documented. Some of the modes are responsible for a large fraction of the kinetic energy flux to the wind turbine region. Surprisingly, more flow structures (POD modes) are needed to capture at least 40% of the turbulent kinetic energy, for which the POD analysis is optimal, than are needed to capture at least 40% of the kinetic energy flux to the turbines. For comparison, we consider the cases of aligned and staggered wind turbine arrays in a neutral atmospheric boundary layer as well as a reference case without wind turbines. While the general characteristics of the flow structures are robust, the net kinetic energy entrainment to the turbines depends on the presence and relative arrangement of the wind turbines in the domain.

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 there. The results show that improving the rate of vertical kinetic energy entrainment into wind turbine arrays is a standing challenge and would require modifying the large-scale structures of the flow. Such an optimization would in the future aid recovery of the wind turbine wake towards conditions corresponding to the undisturbed atmospheric boundary layer.