the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Generalized analytical body force model for actuator disc computations of wind turbines
Abstract. A new generalized analytical model for representing body forces in numerical actuator disc models of wind turbines is proposed and compared to results from a Blade Element Momentum (BEM) model. The model is an extension of a previously developed load model, which was based on the rotor disc being subject to a constant circulation, modified for tip and root effects, corresponding to an optimum design case. By adding a parabolic circulation distribution, corresponding to a solid-body approach of the flow in the near-wake, it is possible to take into account losses associated with off-design cases, corresponding to pitch regulation at high wind speeds. The advantage of the model is that it does not depend on any detailed knowledge concerning the actual wind turbine being analysed, but only requires information about the thrust coefficient and tip speed ratio. The model is validated for different wind turbines operating under a wide range of operating conditions. The comparisons show generally an excellent agreement with the BEM model even at very small thrust coefficients and tip speed ratios.
Jens Nørkær Sørensen
Status: closed
-
RC1: 'Comment on wes-2022-108', Sven Schmitz, 03 Jan 2023
Review of WES-2022-108
J. N. Sorensen : “Generalized Analytical Body Force Model For Actuator Disc Computations of Wind Turbines”
Leonardo DaVinci once said: “Simplicity is the ultimate sophistication.” This seems to readily apply to the proposed generalized analytical body force model presented in the manuscript. Great work that has potential for significant impact. Well done.
Scientific Significance: The manuscript presents a generalized actuator disc (AD) model for use in wind farm simulations. The novel scientific aspect of the extended (i.e. generalized) model is that it enables AD methods for use at off-design (Region III) wind speeds, as opposed to be only valid for design (i.e. close to optimal) conditions in Region II. This merits not only publication in WES but also is potentially impactful to the broader community on wind farm wake modeling.
Scientific Quality: The mathematical methods used in the manuscript appear to be correct. All relevant information is given for the reader to implement the proposed model in independent analyses. The work is of the highest scientific quality, demonstrating physical insight into wind turbine aerodynamics at off-design conditions.
Presentation Quality: Good writing style w/o being excessive in the description of background, motivation, mathematical formulation, graphs etc. Very well done.
Minor Comments:
- Typos in lines 144, 282, 285, 326. Please doublecheck.
- Section 3.1: The author may consider revising the paragraph describing ‘tuning’ of the model. The reviewer would hope for a more physics-based explanation/description; at a minimum, what range of values are expected for S0 and why?
- Page 14: Discussion of tangential loading seen in Figs. 5-7. The explanation in line 329 “for some unknown reason” is incomplete. Here again, the reviewer would expect some physics-based explanation for the observation. For example, is there a distinct difference in the design of the root region for the V27 in comparison to the V52 and NM80 ? If yes, then the behavior of the tangential loads can probably be explained. Please investigate a little further.
Citation: https://doi.org/10.5194/wes-2022-108-RC1 -
RC2: 'Comment on wes-2022-108', Anonymous Referee #2, 21 Apr 2023
Dear Editor, dear Jens,
It's a pleasure to read this work.
Here are my general comments:
This manuscript presents an extension of an existing analytical body force model for a Joukowsky rotor with constant bound circulation, previously developed by the author, to a contemporary pitch-regulated rotor with variable circulation by introducing a parabolic circulation distribution. The parameters for the parabolic circulation distribution were derived through the characterization of various wind turbine models. The accuracy of the final model was verified against Blade Element Momentum (BEM) results. This simple analytical model has potential utility for the wind energy industry.
I have two general comments regarding the manuscript:
- To enhance readers' comprehension of the derivation in section 2.2, it may be beneficial to include a schematic plot with coordinates.
- As the parameter S0 is tuned on the three rotors of V27, V52, NM80. It would be great to present the verification results for a different wind turbine model to show the robustness of the analytical model.
Please refer to the attached pdf file for some additional comments.
Good luck with the revision!
-
AC1: 'Comment on wes-2022-108', Jens Nørkær Sørensen, 06 May 2023
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2022-108/wes-2022-108-AC1-supplement.pdf
Status: closed
-
RC1: 'Comment on wes-2022-108', Sven Schmitz, 03 Jan 2023
Review of WES-2022-108
J. N. Sorensen : “Generalized Analytical Body Force Model For Actuator Disc Computations of Wind Turbines”
Leonardo DaVinci once said: “Simplicity is the ultimate sophistication.” This seems to readily apply to the proposed generalized analytical body force model presented in the manuscript. Great work that has potential for significant impact. Well done.
Scientific Significance: The manuscript presents a generalized actuator disc (AD) model for use in wind farm simulations. The novel scientific aspect of the extended (i.e. generalized) model is that it enables AD methods for use at off-design (Region III) wind speeds, as opposed to be only valid for design (i.e. close to optimal) conditions in Region II. This merits not only publication in WES but also is potentially impactful to the broader community on wind farm wake modeling.
Scientific Quality: The mathematical methods used in the manuscript appear to be correct. All relevant information is given for the reader to implement the proposed model in independent analyses. The work is of the highest scientific quality, demonstrating physical insight into wind turbine aerodynamics at off-design conditions.
Presentation Quality: Good writing style w/o being excessive in the description of background, motivation, mathematical formulation, graphs etc. Very well done.
Minor Comments:
- Typos in lines 144, 282, 285, 326. Please doublecheck.
- Section 3.1: The author may consider revising the paragraph describing ‘tuning’ of the model. The reviewer would hope for a more physics-based explanation/description; at a minimum, what range of values are expected for S0 and why?
- Page 14: Discussion of tangential loading seen in Figs. 5-7. The explanation in line 329 “for some unknown reason” is incomplete. Here again, the reviewer would expect some physics-based explanation for the observation. For example, is there a distinct difference in the design of the root region for the V27 in comparison to the V52 and NM80 ? If yes, then the behavior of the tangential loads can probably be explained. Please investigate a little further.
Citation: https://doi.org/10.5194/wes-2022-108-RC1 -
RC2: 'Comment on wes-2022-108', Anonymous Referee #2, 21 Apr 2023
Dear Editor, dear Jens,
It's a pleasure to read this work.
Here are my general comments:
This manuscript presents an extension of an existing analytical body force model for a Joukowsky rotor with constant bound circulation, previously developed by the author, to a contemporary pitch-regulated rotor with variable circulation by introducing a parabolic circulation distribution. The parameters for the parabolic circulation distribution were derived through the characterization of various wind turbine models. The accuracy of the final model was verified against Blade Element Momentum (BEM) results. This simple analytical model has potential utility for the wind energy industry.
I have two general comments regarding the manuscript:
- To enhance readers' comprehension of the derivation in section 2.2, it may be beneficial to include a schematic plot with coordinates.
- As the parameter S0 is tuned on the three rotors of V27, V52, NM80. It would be great to present the verification results for a different wind turbine model to show the robustness of the analytical model.
Please refer to the attached pdf file for some additional comments.
Good luck with the revision!
-
AC1: 'Comment on wes-2022-108', Jens Nørkær Sørensen, 06 May 2023
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2022-108/wes-2022-108-AC1-supplement.pdf
Jens Nørkær Sørensen
Jens Nørkær Sørensen
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 264 | 108 | 12 | 384 | 6 | 4 |
- HTML: 264
- PDF: 108
- XML: 12
- Total: 384
- BibTeX: 6
- EndNote: 4
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1