Publications about the actuator disc

Early in 2023, Google Scholar gave a total of 228 publications mentioning my name as a (co-)author, with 5750 citations. Most are in peer-reviewed journals. For the majority of these publications, the credits go to the authors who appear first in the list of authors, usually the PhD students. This page does not list these publications; they can be found in scientific databases, archives of scientific journals and in

Cover picture: The Red Mill, Piet Mondriaan, 1911, collection Kunstmuseum Den Haag,
 ©2022 Mondrian/Holtzman Trust
Cover picture: The Red Mill, Piet Mondriaan, 1911, collection Kunstmuseum Den Haag, ©2022 Mondrian/Holtzman Trust

This page contains publications about my own research into the actuator disc, which is the oldest model for the propeller of a ship or airplane, and for the rotor of a wind turbine, helicopter or drone. Some related articles are also included in the table below, while publications that have been overwritten by following or found to be unusable, have been omitted. Several of the publications are published as Open Access, so can be downloaded directly and free of charge. Some papers are not open access but free to read, for the others a subscription with the publisher of the journal or book is required.

The results of all publications except [12] are included in the Open Access book 'The fluid dynamic basis for actuator disc and rotor theory', [13 in the table below]. A much shorter version for wind energy applications is published as chapter in the Handbook of Wind Energy Aerodynamics [11].

The book [13] covers all research topics of the preceding papers, except [12] which treats the existence and impact of (non-)conservative body forces in general, so not limited to rotary flows as is done in [5]. It is advised to use the book as entrance to the research topics, using the papers for more details, because:

  • The treatment and description in the book is believed to be better or more mature than in the papers.
  • Some corrections appeared to be necessary, see [13] page iv and appendix D.

I am very glad to note that as of March 2024, the 2 editions of the book have been downloaded 1700 times.

In case you have questions or remarks about one of the publications, please contact me by mail.

author(s)/year title publication
1 G.A.M. van Kuik,
The flow induced by Prandtl's self-similar vortex sheet spirals at infinite distance from the spiral kernel. European Journal of Mechanics - B/Fluids, 23(4): 607-616,
DOI: 10.1016/j.euromechflu.2004.01.002
2 G.A.M. van Kuik,
The Lanchester - Betz - Joukowsky limit. Wind Energy, 10(3): 289-291.
DOI: 10.1002/we.218
download from WE
3 G.A.M. van Kuik,
A steady solution for Prandtl's self similar vortex sheet spirals. European Journal of Mechanics - B/Fluids, 28(2): 296-298,
DOI: 10.1016/j.euromechflu.2008.05.007
4 V.L. Okulov,
G.A.M. van Kuik,
The Betz-Joukowsky limit: on the contribution to rotor aerodynamics by the British, German and Russian scientific schools. Wind Energy, 15: 335-344,
DOI: 10.1002/we.464
Free to read at WE
5 G.A.M. van Kuik ,
D. Micallef,
I. Herraez,
A.H. van Zuijlen,
D. Ragni, 2014
The role of conservative forces in rotor aerodynamics. Journal of Fluid Mechanics, 750: 284-315,
DOI: 10.1017/jfm.2014.256
6 G.A.M. van Kuik,
J.N. Sørensen,
V.L. Okulov, 2015
Rotor theories by Professor Joukowsky: Momentum Theories. Progress in Aerospace Sciences, 73:1-18,
DOI: 10.1016/j.paerosci.2014.10.001
7 G.A.M. van Kuik,
W. Yu,
S. Sarmast,
S. Ivanell, 2015
Comparison of actuator disc and Joukowsky rotor flows, to explore the need for a tip correction. Journal of Physics Conference Series, 625:012013,
DOI: 10.1088/1742-6596/625/1/012013
download from JoP
8 G.A.M. van Kuik,
L.E.M. Lignarolo, 2016
Potential flow solutions for for energy extracting actuator disc flows. Wind Energy, 19: 1391-1406,
DOI: 10.1002/we.1902
Free to read at WE
9 G.A.M. van Kuik, 2017 Joukowsky actuator disc momentum theory. Wind Energy Science, 2:307-316,
DOI: 10.5194/wes-2-307-2017
download from WES
10 G.A.M. van Kuik, 2020 On the velocity at wind turbine and propeller actuator discs. Wind Energy Science, 5:855-865,
DOI: 10.5194/wes-5-855-2020
download from WES
11 G.A.M. van Kuik, 2021 The Actuator Disc concept. chapter in the Handbook of Wind Energy Aerodynamics, eds. B. Stroevesandt, G. Schepers, P. Fuglsang, S. Yuping, 1-49, Springer Cham,
DOI: 10.1007/978-3-030-05455-7_2-2
12 G.A.M. van Kuik, 2022 On (non-)conservative body force fields generating vorticity and converting energy. Journal of Fluid Mechanics, 941: A64 1-17,
DOI: 10.1017/jfm.2022.317
download from JFM
13 G.A.M. van Kuik, 2022 The Fluid Dynamic Basis for Actuator Disc and Rotor Theories, revised second edition. IOS Press, Amsterdam,
DOI: 10.3233/STAL9781643682792
download from IOS Press Ebooks or TU-Delft

In section 1.4 of the book [13], 14 research questions have been formulated. Each chapter ends with a section Evaluation, in which answers to these questions have been formulated.

The following table is structured differently, based on key words or names of topics used in the rotor aerodynamics literature:

brief introduction paper book [13]
the Betz-Joukowsky limit In [2] the re-discovery of Joukowsky's paper was published. In [4] it was argued that Lanchaster did not draw the same conclusion as Betz and Joukowsky, as he considered the limit as one of the possible outcomes, not as thé result. [2]
ch. 1
the actuator disc as valid model for a rotor Numerically, experimentally as well as analytically the actuator disc is shown to represent a rotor. The axial velocity at the rotor blade position agrees well with the disc velocity distribution. [7] ch. 4
the performance of discs with and without swirl Potential flow calculations have confirmed the one dimensional momentum theory. The two-dimensional theory, so with torque applied to the flow, corrected the result for the rotational speed going to zero: previous publications showed the nice but impossible result of the efficiency becoming infinite. It is shown to be zero for zero rotational speed, as it should be. [8]


ch.5 (no torque),
ch. 6 (with)
the velocity distribution For discs with and without swirl the distribution is calculated, with the observation that √(vaxial2+vradial2), the velocity in the meridional plan, is constant except very close to the disc edge. An explanation is provided. [10] ch. 7
the edge singularity The potential flow calculations show a singular behaviour of the wake boundary vortex sheet strength. This singularity does not carry a load. Analytical studies showed that a solution of the vortex sheet near the edge, found in literature, is not applicable, [3]. A spin-off was the analysis of vortex flows decribed by Prandtl, [1], giving a new interpretation. [8]
the edge singularity (2) I also publised about the edge singularity. The paper has the title 'An inconsistency in the actuator disc momentum theory'. However, the title is not correct as the paper contains a mathematical error. After having found this error, I published a correction: 'No inconsistency in the actuator disc momentum theory'.
the momentum theory per annulus It is known that the disc momentum theory applied to an annulus gives incorrect results. Including the pressure acting at the boundary of the annulus in the momentum theory gives very good agreement with the calculations. [8]
the tip correction The combination of constant axial velocity plus a tip correction, as applied in Blade Element Momentum methods, results in a distribution of the axial velocity which resembles well the actuator disc distribution. [7] ch. 9
conservative or non-conservative loads The momentum theory per annulus (including the pressure at its boundary) as well as the momentum theory including torque, show a distinction between loads performing work, and loads not doing so, or: between non-conservative and conservative loads. [5]
ch. 2
the tip vortex Some experiments show the tip vortex of a wind turbine rotor moving to a lower radius before wake expansion starts. It is shown that this is due to conservative loads acting on the blade tip. [5] ch. 8