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

Moens, Maud; Duponcheel, Matthieu; Winckelmans, Grégoire; Chatelain, Philippe

doi:10.1002/we.2192

Cited by 25 publications

(38 citation statements)

References 37 publications

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“…A solution for the wake of Betz's rotor, still restricted to lightly loaded propellers, was presented by Goldstein (1929). The non-linear solution, so including wake deformation, was published by Okulov (2014) and Wood G. A. M. van Kuik: The velocity at the actuator disc (2015). A comparison of the models of Betz and Joukowsky for rotors was presented by Okulov et al (2015, chap.…”

Section: Introductionmentioning

confidence: 99%

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On the velocity at wind turbine and propeller actuator discs

Kuik

2020

Wind Energ. Sci.

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Abstract. The first version of the actuator disc momentum theory is more than 100 years old. The extension towards very low rotational speeds with high torque for discs with a constant circulation became available only recently. This theory gives the performance data like the power coefficient and average velocity at the disc. Potential flow calculations have added flow properties like the distribution of this velocity. The present paper addresses the comparison of actuator discs representing propellers and wind turbines, with emphasis on the velocity at the disc. At a low rotational speed, propeller discs have an expanding wake while still energy is put into the wake. The high angular momentum of the wake, due to the high torque, creates a pressure deficit which is supplemented by the pressure added by the disc thrust. This results in a positive energy balance while the wake axial velocity has lowered. In the propeller and wind turbine flow regime the velocity at the disc is 0 for a certain minimum but non-zero rotational speed. At the disc, the distribution of the axial velocity component is non-uniform in all actuator disc flows. However, the distribution of the velocity in the plane containing the axis, the meridian plane, is practically uniform (deviation <0.2 %) for wind turbine disc flows with tip speed ratio λ>5, almost uniform (deviation ≈2 %) for wind turbine disc flows with λ=1 and propeller flows with advance ratio J=π, and non-uniform (deviation 5 %) for the propeller disc flow with wake expansion at J=2π. These differences in uniformity are caused by the different strengths of the singularity in the wake boundary vorticity strength at its leading edge.

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Section: Introductionmentioning

confidence: 99%

“…Recent research aims for deriving efficient tip corrections (see e.g. Moens and Chatelain, 2018;Zhong et al, 2019) or for configurations including a hub (Bontempo and Manna, 2016) or duct (Dighe et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

On the velocity at wind turbine and propeller actuator discs

Kuik

2020

Wind Energ. Sci.

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“…The model for the recovery of U e is provided in "Appendix A." A similar procedure was proposed by [25] and [29] for actuator methods.…”

Section: Reconstruction Of the Effective Upstream Velocity U Ementioning

confidence: 99%

An immersed lifting and dragging line model for the vortex particle-mesh method

Caprace

Winckelmans

Chatelain

2020

Theor. Comput. Fluid Dyn.

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The numerical study of the wake of full-scale slender devices such as aircraft wings and wind turbine blades requires high-fidelity large eddy simulation tools. The broad spectrum of scales involved entails the use of coarse-grain models for the devices. Actuator disk or line methods have been developed for that purpose, and are to date the most employed in that context. These methods transfer the force from the device to the fluid using 3D mollification functions. A novel immersed lifting and dragging line method is here presented, together with its implementation in a hybrid vortex particle-mesh flow solver. The line models the effect of blades or wings on the flow through the generation of vorticity, in a Lagrangian manner. This has several advantages over the treatment inherent to actuator methods: The absence of mollification in the spanwise direction and the relaxation of the classical Courant-Friedrichs-Lewy condition contribute to keeping the accuracy and the efficiency at a high level. The method is thoroughly verified against theory using results on various airfoils and wings. Finally, the efficiency of the approach is illustrated with the simulation of the wake of an elliptical wing. The role of parasitic drag in the development of wake instabilities is pointed out, by comparing configurations with none, moderate and high profile drag. In the last case, the simulation captures the fine scales vortex dynamics and the establishment of a turbulent wake over a length of 30 wing spans.

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“…Recent research aims for deriving efficient tip corrections, see e.g. Moens and Chatelain (2018), Zhong et al (2019), or for configurations including a hub, Bontempo and Manna (2016), or duct, Dighe et al (2019).…”

Section: Introductionmentioning

confidence: 99%

On the velocity at wind turbine and propeller actuator discs

Kuik¹

2020

Preprint

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Abstract. The first version of the actuator disc momentum theory is more than 100 years old. The extension towards very low rotational speeds with high torque for discs with a constant circulation, became available only recently. This theory gives the performance data like the power coefficient and average velocity at the disc. Potential flow calculations have added flow properties like the distribution of this velocity. The present paper addresses the comparison of actuator discs representing propellers and wind turbines, with emphasis on the velocity at the disc. At a low rotational speed, propeller discs have an expanding wake while still energy is put into the wake. The high angular momentum of the wake, due to the high torque, creates a pressure deficit which is supplemented by the pressure added by the disc thrust. This results in a positive energy balance while the wake axial velocity has lowered. In the propeller and wind turbine flow regime the velocity at the disc is 0 for a certain minimum but non-zero rotational speed. At the disc, the distribution of the axial velocity component is non-uniform in all flow states. However, the distribution of the velocity in the plane containing the axis, the meridian plane, is practically uniform (deviation approximately 0.2 %) for wind turbine disc flows with tip speed ratio λ > 5, almost uniform (deviation 2 %) for wind turbine disc flows with λ = 1 and propeller flows with advance ratio J = Π, and non-uniform (deviation 5 %) for the propeller disc flow with wake expansion at J = 2 Π. These differences in uniformity are caused by the different strengths of the singularity in the wake boundary vorticity strength at its leading edge.

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

Cited by 25 publications

References 37 publications

On the velocity at wind turbine and propeller actuator discs

On the velocity at wind turbine and propeller actuator discs

An immersed lifting and dragging line model for the vortex particle-mesh method

On the velocity at wind turbine and propeller actuator discs

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