Vortex methods to answer the need for improved understanding and modelling of tip‐loss factors

Branlard, Emmanuel; Dixon, Kristian; Gaunaa, Mac

doi:10.1049/iet-rpg.2012.0283

Cited by 27 publications

(19 citation statements)

References 12 publications

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“…Investigations have been performed to improve this model or to create alternatives to this classical correction, based on higher fidelity methods. A data base of tip‐loss corrections was elaborated by Branlard et al using a lifting‐line code and aimed at replacing the Glauert tip‐loss factor in an adapted BEM theory. Schmitz and Maniaci added a simple modification to the classical tip‐loss correction that led to improved BEM prediction at the blade tip.…”

Section: Methodsmentioning

confidence: 99%

“…It is better highlighted by comparing the computed tip‐loss factor in AD‐C‐EV to ones extracted from the VPM simulations (Figure ). The methodology of Branlard et al is used to express the normal and the tangential tip‐loss factors in the VPM approach

f_{a} = \frac{{(⟨⟩, a)}_{θ}}{a_{B}} and f_{a^{'}} = \frac{{(⟨⟩, a^{'})}_{θ}}{a_{B}^{'}},

where

{(⟨⟩ .)}_{θ}

represents the azimuthal average. a B and

a_{B}^{'}

are extracted from the VPM blade velocities, a B =1− u n , B / U ∞ and a ′ B = u θ , B /Ω r , while averaged induction factors are obtained in the same way but by using the azimuthally averaged velocity field at the rotor position.…”

Section: The Joukowksy Rotormentioning

confidence: 99%

“…The analytical tip‐loss factor appears to overestimate the losses, mainly on the outboard part of the blade. This agrees with observations made in the work of Branlard et al, where the Glauert tip‐loss correction computed in a BEM approach over predicted the losses extracted from a lifting line method. This most probably comes from the Glauert tip‐loss correction itself, which relies on strong assumptions.…”

Section: The Joukowksy Rotormentioning

confidence: 99%

“…The contribution of the wake to the induced velocities at the rotor level thus differs from that due to a finite number of tip vortices. The impact is relatively small for rotors operating at high loading and high tip‐speed ratios, because the tip and root vortices shed by actual blades are very close to each other, leading to a flow field at the rotor level and a wake topology similar to those of an AD. Advanced AD methods are thus claimed by some authors to capture the induced velocities in a satisfactory manner .…”

Section: Introductionmentioning

confidence: 99%

“…One solution consists in using the typical Glauert tip‐loss factor, commonly added in the BEM methods (a review of this factor and its variants was made by Branlard) and in adapting its implementation for AD in Navier‐Stokes equations . This correction and its alternative versions are well adapted for the BEM implementation and often applied on the induction factors that are naturally available in this theory. Still, their use within an advanced AD model requires to compute these factors at the very disk from the local velocity field .…”

Section: Introductionmentioning

confidence: 99%

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An actuator disk method with tip‐loss correction based on local effective upstream velocities

et al. 2018

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This work aims at assessing the performance of a tip‐loss correction for advanced actuator disk (AD) methods coupled to large eddy simulation and making this correction possible in a wind farm configuration. The classical Glauert tip‐loss factor, commonly used in the blade element momentum method, is added here to correct the tip and the root induced velocities at the rotor. However, it requires a reference upstream velocity, which is problematic to define in complex flows, such as in wind farms. A methodology is proposed here to infer an effective upstream velocity local to each disk element, based on the one‐dimensional momentum theory and using only the local data at the rotor. This estimation is verified through a set of simulations, leading to good results in spite of the crude assumptions of the one‐dimensional momentum theory. This AD supplemented with the tip‐loss correction is compared with a high fidelity vortex particle‐mesh method, through the simulations in uniform wind of a constant circulation wind turbine and of a more realistic machine, the NREL‐5MW rotor. The results show that the AD behavior is clearly improved by the addition of a tip‐loss factor and the potential errors on the effective upstream velocity estimation have a moderate impact on the tip‐loss correction.

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Section: Methodsmentioning

confidence: 99%

f_{a} = \frac{{(⟨⟩, a)}_{θ}}{a_{B}} and f_{a^{'}} = \frac{{(⟨⟩, a^{'})}_{θ}}{a_{B}^{'}},

where

{(⟨⟩ .)}_{θ}

represents the azimuthal average. a B and

a_{B}^{'}

Section: The Joukowksy Rotormentioning

confidence: 99%

Section: The Joukowksy Rotormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An actuator disk method with tip‐loss correction based on local effective upstream velocities

et al. 2018

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Cylindrical vortex wake model: right cylinder

Branlard

Gaunaa

2014

Wind Energy

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The vortex system consisting of a bound vortex disk, a root vortex and a vortex cylinder as introduced by Joukowski in 1912 is further studied in this paper. This system can be used for simple modeling of rotors (e.g. wind turbines) with infinite number of blades and finite tip-speed ratios. For each vortex element, the velocity components in all directions and in the entire domain are computed analytically in a novel approach. In particular, the velocity field from the vortex actuator disk is derived for the first time. The induction from the entire vortex system is studied and is seen to recall results from 1D momentum theory. It is shown that a superposition of concentric cylindrical systems predicts the independence of annuli, which is assumed in blade element theory and stream-tube analyses. A simple example of application for the estimation of the velocity deficit upstream of a wind turbine is provided.

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Cylindrical vortex wake model: skewed cylinder, application to yawed or tilted rotors

Branlard

Gaunaa

2015

Wind Energy

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A vortex system consisting of a bound vortex disk, a root vortex and a vortex cylinder is presented and applied for skewed wake situations. Both the longitudinal and tangential components of vorticity of the cylinder are considered. A subset of this system leads to a model, which is commonly used in Blade Element Momentum method codes for yawed conditions. Here, all the components of the full vortex system are analyzed in view of extending Blade Element Momentum models. The main assumptions of the current study are a constant uniform circulation, an infinite number of blades, an un-expanding wake shape and a finite tip-speed ratio. The investigation remains within the context of inviscid potential flow theory. The model is derived for horizontal-axis rotors in general, but results are presented for wind-turbine applications. For each vortex element, the velocity components in all directions are computed analytically or semi-analytically for the entire domain. Simplified engineering models are provided to ease the evaluation of velocities in the rotor plane. The predominant velocity components are assessed.

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Vortex methods to answer the need for improved understanding and modelling of tip‐loss factors

Cited by 27 publications

References 12 publications

An actuator disk method with tip‐loss correction based on local effective upstream velocities

An actuator disk method with tip‐loss correction based on local effective upstream velocities

Cylindrical vortex wake model: right cylinder

Cylindrical vortex wake model: skewed cylinder, application to yawed or tilted rotors

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