An entrainment‐based model for annular wakes, with applications to airborne wind energy

Kaufman-Martin, Sam; Naclerio, Nicholas D.; May, Pedro; Luzzatto‐Fegiz, Paolo

doi:10.1002/we.2679

Cited by 8 publications

(7 citation statements)

References 36 publications

(70 reference statements)

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“…The power equations for Fly-Gen and Ground-Gen AWESs are then derived by reducing the incoming wind of the induced velocities. They find that Fly-Gen AWESs have higher power generation potential compared to Ground-Gen. Kaufman-Martin et al (2021); Kheiri et al (2022) and Karakouzian et al (2022) study, with the aim of understanding the interaction of AWESs in a wind farm, the downstream AWES wake shape and characteristics with momentum and mass conservation considerations, finding a good agreement with CFD results. Gaunaa et al (2020) point out that using momentum theory to evaluate the induction of an AWES, which is described by 3D polars, is not physically consistent.…”

Section: Introductionmentioning

confidence: 63%

Vortex model of the airborne wind energy systems aerodynamic wake

Trevisi¹,

Riboldi²,

Croce³

2023

Preprint

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Abstract. Understanding and modelling the aerodynamic wake of airborne wind energy systems (AWESs) is crucial for estimating the performance and defining the design of such systems, as tight trajectories increase induced velocities, and thus decrease the available power, while unnecessarily large trajectories increase power losses due to the gravitational potential energy exchange. The aerodynamic wake is here studied with vortex methods, as momentum methods cannot be applied to AWESs in a physically consistent way. The velocities induced at the AWES from a generic helicoidal vortex filament, trailed by a position on the AWES wing, is modelled with an expression for the near vortex filament and one for the far vortex filament. The near vortex filament is modelled as the first half rotation of the helicoidal filament, where its axial component is neglected. The induced drag due to the near wake, built up from near vortex filaments, is found to be similar to the induced drag the AWES would have in forward flight. The far wake is modelled as two semi-infinite vortex rings cascades with opposite intensity. An approximate solution for the induced axial velocity at the AWES is given as function of the radial (known) and axial (unknown) position of the vortex rings. An explicit and an implicit closure model are introduced to link the axial position of the vortex rings with the other quantities of the model. The aerodynamic model, using the implicit closure model for the far wake, is validated with the lifting line free vortex wake method implemented in QBlade. The model is suitable to be used in time-marching aero-servo-dynamic-elastic simulations and in design and optimization studies.

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Section: Introductionmentioning

confidence: 63%

Vortex model of the airborne wind energy systems aerodynamic wake

Trevisi¹,

Riboldi²,

Croce³

2023

Preprint

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“…We adopt the method proposed in [27] to obtain the wake radii and the average wake velocity from the CFD results presented in Section 2. The wake boundary (or width) in the radial direction at any streamwise coordinate ξ is considered as the point where the flow velocity reaches 99% of the freestream velocity-Kaufman-Martin et al [31] considered the surface where the flow velocity reached the freestream velocity as the wake boundary. The average wake velocity was also obtained by integrating the area under the velocity profile between the wake inner and outer radii.…”

Section: Comparison Between Cfd and Analytical Resultsmentioning

confidence: 99%

“…and the dimensionless counterpart of Equation ( 9) can be written as A simplifying assumption is to consider the flow velocity in the inner region to remain constant and equal to the freestream velocity, i.e., υ i = υ c = 1; a similar assumption was made in [31]. From CFD results presented in Section 2.4, it is seen that υ c may actually reach values above 1, which means that flow may accelerate inside the inner region; nevertheless, this increase of flow velocity is minimal and still the assumption of υ c = 1 may be reasonable.…”

Section: Cv1 Axis Of Rotation/symmetrymentioning

confidence: 99%

“…Unlike conventional wind turbines, there has been very little effort to develop analytical wake models for CKPSs. Only recently, Kaufman-Martin et al [31] developed a model based on the entrainment hypothesis for annular wakes [32]. In general, a system of three ordinary differential equations should be solved simultaneously to find the variation of the wake radii and flow velocity.…”

Section: Introductionmentioning

confidence: 99%

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Aerodynamic Performance and Wake Flow of Crosswind Kite Power Systems

Kheiri

Victor²,

Rangriz

et al. 2022

Energies

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This paper presents some results from a computational fluid dynamics (CFD) model of a multi-megawatt crosswind kite spinning on a circular path in a straight downwind configuration. The unsteady Reynolds averaged Navier-Stokes equations closed by the k−ω SST turbulence model are solved in the three-dimensional space using ANSYS Fluent. The flow behaviour is examined at the rotation plane, and the overall (or global) induction factor is obtained by getting the weighted average of induction factors on multiple annuli over the swept area. The wake flow behaviour is also discussed in some details using velocity and pressure contour plots. In addition to the CFD model, an analytical model for calculating the average flow velocity and radii of the annular wake downstream of the kite is developed. The model is formulated based on the widely-used Jensen’s model which was developed for conventional wind turbines, and thus has a simple form. Expressions for the dimensionless wake flow velocity and wake radii are obtained by assuming self-similarity of flow velocity and linear wake expansion. Comparisons are made between numerical results from the analytical model and those from the CFD simulation. The level of agreement was found to be reasonably good. Such computational and analytical models are indispensable for kite farm layout design and optimization, where aerodynamic interactions between kites should be considered.

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“…For individual systems, recent investigations of flow induction and wake effects were performed, mainly considering axissymmetric AWES configurations in uniform inflows using either analyses based on momentum theory (Leuthold et al, 2017;De Lellis et al, 2018), vortex theory (Leuthold et al, 2019;Gaunaa et al, 2020) or the entrainment hypothesis (Kaufman-Martin et al, 2021), or high-fidelity CFD simulations (Haas and Meyers, 2017;Kheiri et al, 2018). Further numerical investigations of large-scale airborne wind energy systems in the atmospheric boundary layer (ABL) (Haas et al, 2019b) have shown that the wake development downstream of the system is considerable, hence suggesting that wake effects of utility-scale airborne wind energy systems can not be neglected when operating in parks.…”

Section: Introductionmentioning

confidence: 99%

Large-eddy simulation of airborne wind energy farms

Haas

Schutter

Diehl

et al. 2021

Preprint

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Abstract. The future utility-scale deployment of airborne wind energy technologies requires the development of large-scale multi-megawatt systems. This study aims at quantifying the interaction between the atmospheric boundary layer (ABL) and large-scale airborne wind energy systems operating in a farm. To that end, we present a virtual flight simulator combining large-eddy simulations to simulate turbulent flow conditions and optimal control techniques for flight-path generation and tracking. The two-way coupling between flow and system dynamics is achieved by implementing an actuator sector method that we pair to a model predictive controller. In this study, we consider ground-based power generation pumping-mode AWE systems (lift-mode AWES) and on-board power generation AWE systems (drag-mode AWES). For the lift-mode AWES, we additionally investigate different reel-out strategies to reduce the interaction between the tethered wing and its own wake. Further, we investigate AWE parks consisting of 25 systems organized in 5 rows of 5 systems. For both lift- and drag-mode archetypes, we consider a moderate park layout with a power density of 10 MW km−2 achieved at a rated wind speed of 12 m s−1. For the drag-mode AWES, an additional park with denser layout and power density of 28 MW km−2 is also considered. The model predictive controller achieves very satisfactory flight-path tracking despite the AWE systems operating in fully waked, turbulent flow conditions. Furthermore, we observe significant wake effects for the utility-scale AWE systems considered in the study. Wake-induced performance losses increase gradually through the downstream rows of systems and reach in the last row of the parks up to 17 % for the lift-mode AWE park and up to 25 % and 45 % for the moderate and dense drag-mode AWE parks, respectively. For an operation period of 60 minutes at a below-rated reference wind speed of 10 m s−1, the lift-mode AWE park generates about 84.4 MW of power, corresponding to 82.5 % of the power yield expected when AWE systems operate ideally and interaction with the ABL is negligible. For the drag-mode AWE parks, the moderate and dense layouts generate about 86.0 MW and 72.9 MW of power, respectively, corresponding to 89.2 % and 75.6 % of the ideal power yield.

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An entrainment‐based model for annular wakes, with applications to airborne wind energy

Cited by 8 publications

References 36 publications

Vortex model of the airborne wind energy systems aerodynamic wake

Vortex model of the airborne wind energy systems aerodynamic wake

Aerodynamic Performance and Wake Flow of Crosswind Kite Power Systems

Large-eddy simulation of airborne wind energy farms

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