the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Nov 2025
Optimization of Dual Rotor Wind Turbine with Double Rotational Armature Using Configurable BEM Method, Validated by Wind Tunnel Measurement
Abstract. Small wind turbines (SWTs) face significant challenges in achieving commercial viability due to lower efficiency and higher energy costs compared to utility-scale systems and competing renewable technologies. Counter-rotating dual rotor wind turbines (CR-DRWTs) with dual rotational armature configurations offer a potential pathway for efficiency improvements through doubled direct drive power, minimal mechanical complexity, and reduced noise characteristics suitable for urban applications. This study investigated the aerodynamic performance of a 1.6 m diameter CR-DRWT through wind tunnel testing at the Centre Scientifique et Technique du Bâtiment (CSTB) in Nantes, France, at wind speeds ranging from 4 to 15 m/s. Enhanced instrumentation including RPM and pitch angle sensors provided detailed operational measurements. The turbine achieved maximum power output of 1014 W and a peak power coefficient (CP) of 0.33, and demonstrates reliable self-starting capability at 3.5 m/s. A Blade Element Momentum (BEM) model was adapted for dual rotational armature systems and validated against experimental data, showing good overall agreement. Differential evolution optimization algorithms identified optimal operational parameters with upstream rotor pitch angles of 9.8° and downstream angles of 0.6°, both operating at tip-speed ratios near 6. The optimized configuration predicted a theoretical maximum CP of 0.51, indicating substantial performance improvement potential. The study demonstrates that dual rotational armature CR-DRWT eliminates gearbox requirements while maintaining competitive performance, offering a mechanically simpler and potentially more cost-effective solution for small-scale wind energy applications, particularly in urban environments where compactness and low noise are critical design constraints.
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Status: final response (author comments only)
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RC1: 'Comment on wes-2025-244', Anonymous Referee #1, 18 Dec 2025
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AC1: 'Comment on wes-2025-244', Niels Adema, 18 Apr 2026
We would like to thank both referees for reviewing the manuscript and providing valuable critiques and insight to the work.
The updated manuscript now includes their comments. And below we provide a description of the changes made.
The main changes:
We appreciate referee 2 pointing out that our method for calculating torque balance in the extended BEM model was wrong. So, we have now included a loop in the code that only selects operating points where torque balance is present. Which is now also explained in the manuscript. During the sweep optimization we keep this loop such that also there only operating points are valid where torque balance is present. When improving the BEM model we noticed that in our measurements we mixed up the upstream and downstream RPM sensor, we adapted the results table and graphs accordingly. With respect to the electrical losses: we have included the generator efficiency we determined in earlier work specifically in the text, graphs, and model. We agree that the DC load may influence the efficiency of the system, we have mentioned the type and brand of the the load used in the CSTB wind tunnel. And also our process of manual power point tracking by changing the resistance at every wind speed to find the maximum power point (The turbine does not include an MPPT). We have updated the manuscript with the textual changes from the accompanying pdf file from referee 2 as well. Including an update to the third paragraph of the discussion where we now more clearly present a comparison between DRWT and single rotor operation.
We furthermore updated the introduction and abstract according to the suggestions from referee 1. We now emphasize more on the experimental campaign instead of the extended BEM model. In the introduction we include a paragraph on already present BEM models and why we selected Amoretti's. Also in section 2 we tried to make more clear what our extension to their model is. We now state explicitly in the discussion that design methods exist for downstream rotor design and that our mirroring is not optimal. In the explanation of the mechanical turbine design we included more information from previous work to better detail hub design, blade root section, and pitch system. The graphs of the measurements do have error bars as can be seen in the CP plot of the CSTB measurements at low wind speed. We now explain in 3.2 the metric used for the error in the measurements. Rprop is changed to Rrotor (this came from the Amoretti paper). The distance between rotors is explicitly stated. The collective pitch is equal for three blades which is hopefully clear with the inclusion of the pitch system design explanation.
Also as suggested by referee 1 we update the title for put more focus on the experimental part of the study. We did struggle a bit as we also wanted to focus on the extension of Amoretti's BEM model to fit a double rotational armature design. So, we hope we have reached a better balance in he title now.
Finally after proofreading the updated manuscript we included some additional textual changes for clarity. We acknowledge that the present manuscript is a much improved version due to the comments of the referees and would like to thank them for their efforts.
On behalf of the authors,
Niels Adema
Citation: https://doi.org/10.5194/wes-2025-244-AC1
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AC1: 'Comment on wes-2025-244', Niels Adema, 18 Apr 2026
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RC2: 'Comment on wes-2025-244', Anonymous Referee #2, 20 Mar 2026
The paper presents a study on the design optimization and verification of a dual rotor configuration featuring a double rotational armature. The rotor optimization is carried out using as core solver a newly adapted BEM method that accounts for the interaction between the upstream and downstream rotors, coupled with a differential evolution algorithm implemented through SciPy libraries.
The work is both novel and relevant to the wind energy community and, in the reviewer’s opinion, deserves publication in WES. However, I would recommend some revisions to the manuscript based on the comments provided in the accompanying pdf, as well as the key points summarized below:
1) In Section 2.3.4, it is stated that the system is in balance when the two rotors produce equal torque. However, it is unclear how this condition is satisfied through the minimum torque criterion described in Equation (22). While it is understood that the minimum torque governs the system, it is not evident how the balance requirement is satisfied if the operating conditions of the second rotor are not correspondingly adjusted. One would expect an inner iterative loop to be implemented to enforce torque equality between the rotors. Otherwise, the inflow conditions of the downstream rotor may not be physically realistic.
2) A related point is how this balance condition is maintained during the optimization process. The optimizer may select combinations of rotational speeds and pitch angles that do not satisfy the equal-torque requirement. It is therefore unclear how such constraints are enforced within the optimization framework.
3) One aspect that remains somewhat unclear is how the generator and the MPPT system influence the overall operation of the system. For instance, is there any assessment of the electrical losses? These losses are expected to depend on torque and could vary significantly. Furthermore, if the MPPT system is continuously searching for the optimal operating point, the Cp would be expected to remain constant over the whole range of wind speeds, which does not appear to be the case. This suggests that the load connected to the generator may also influence the response of the system.
4) I would say that the third paragraph of the discussion section lacks clarity. Perhaps a computed comparison of the single versus the dual rotor would enhance understanding.
As I mentioned above there several other smaller comments in the accompanied pdf that need to be answered in the rebuttal.
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AC1: 'Comment on wes-2025-244', Niels Adema, 18 Apr 2026
We would like to thank both referees for reviewing the manuscript and providing valuable critiques and insight to the work.
The updated manuscript now includes their comments. And below we provide a description of the changes made.
The main changes:
We appreciate referee 2 pointing out that our method for calculating torque balance in the extended BEM model was wrong. So, we have now included a loop in the code that only selects operating points where torque balance is present. Which is now also explained in the manuscript. During the sweep optimization we keep this loop such that also there only operating points are valid where torque balance is present. When improving the BEM model we noticed that in our measurements we mixed up the upstream and downstream RPM sensor, we adapted the results table and graphs accordingly. With respect to the electrical losses: we have included the generator efficiency we determined in earlier work specifically in the text, graphs, and model. We agree that the DC load may influence the efficiency of the system, we have mentioned the type and brand of the the load used in the CSTB wind tunnel. And also our process of manual power point tracking by changing the resistance at every wind speed to find the maximum power point (The turbine does not include an MPPT). We have updated the manuscript with the textual changes from the accompanying pdf file from referee 2 as well. Including an update to the third paragraph of the discussion where we now more clearly present a comparison between DRWT and single rotor operation.
We furthermore updated the introduction and abstract according to the suggestions from referee 1. We now emphasize more on the experimental campaign instead of the extended BEM model. In the introduction we include a paragraph on already present BEM models and why we selected Amoretti's. Also in section 2 we tried to make more clear what our extension to their model is. We now state explicitly in the discussion that design methods exist for downstream rotor design and that our mirroring is not optimal. In the explanation of the mechanical turbine design we included more information from previous work to better detail hub design, blade root section, and pitch system. The graphs of the measurements do have error bars as can be seen in the CP plot of the CSTB measurements at low wind speed. We now explain in 3.2 the metric used for the error in the measurements. Rprop is changed to Rrotor (this came from the Amoretti paper). The distance between rotors is explicitly stated. The collective pitch is equal for three blades which is hopefully clear with the inclusion of the pitch system design explanation.
Also as suggested by referee 1 we update the title for put more focus on the experimental part of the study. We did struggle a bit as we also wanted to focus on the extension of Amoretti's BEM model to fit a double rotational armature design. So, we hope we have reached a better balance in he title now.
Finally after proofreading the updated manuscript we included some additional textual changes for clarity. We acknowledge that the present manuscript is a much improved version due to the comments of the referees and would like to thank them for their efforts.
On behalf of the authors,
Niels Adema
Citation: https://doi.org/10.5194/wes-2025-244-AC1
-
AC1: 'Comment on wes-2025-244', Niels Adema, 18 Apr 2026
-
AC1: 'Comment on wes-2025-244', Niels Adema, 18 Apr 2026
We would like to thank both referees for reviewing the manuscript and providing valuable critiques and insight to the work.
The updated manuscript now includes their comments. And below we provide a description of the changes made.
The main changes:
We appreciate referee 2 pointing out that our method for calculating torque balance in the extended BEM model was wrong. So, we have now included a loop in the code that only selects operating points where torque balance is present. Which is now also explained in the manuscript. During the sweep optimization we keep this loop such that also there only operating points are valid where torque balance is present. When improving the BEM model we noticed that in our measurements we mixed up the upstream and downstream RPM sensor, we adapted the results table and graphs accordingly. With respect to the electrical losses: we have included the generator efficiency we determined in earlier work specifically in the text, graphs, and model. We agree that the DC load may influence the efficiency of the system, we have mentioned the type and brand of the the load used in the CSTB wind tunnel. And also our process of manual power point tracking by changing the resistance at every wind speed to find the maximum power point (The turbine does not include an MPPT). We have updated the manuscript with the textual changes from the accompanying pdf file from referee 2 as well. Including an update to the third paragraph of the discussion where we now more clearly present a comparison between DRWT and single rotor operation.
We furthermore updated the introduction and abstract according to the suggestions from referee 1. We now emphasize more on the experimental campaign instead of the extended BEM model. In the introduction we include a paragraph on already present BEM models and why we selected Amoretti's. Also in section 2 we tried to make more clear what our extension to their model is. We now state explicitly in the discussion that design methods exist for downstream rotor design and that our mirroring is not optimal. In the explanation of the mechanical turbine design we included more information from previous work to better detail hub design, blade root section, and pitch system. The graphs of the measurements do have error bars as can be seen in the CP plot of the CSTB measurements at low wind speed. We now explain in 3.2 the metric used for the error in the measurements. Rprop is changed to Rrotor (this came from the Amoretti paper). The distance between rotors is explicitly stated. The collective pitch is equal for three blades which is hopefully clear with the inclusion of the pitch system design explanation.
Also as suggested by referee 1 we update the title for put more focus on the experimental part of the study. We did struggle a bit as we also wanted to focus on the extension of Amoretti's BEM model to fit a double rotational armature design. So, we hope we have reached a better balance in he title now.
Finally after proofreading the updated manuscript we included some additional textual changes for clarity. We acknowledge that the present manuscript is a much improved version due to the comments of the referees and would like to thank them for their efforts.
On behalf of the authors,
Niels Adema
Citation: https://doi.org/10.5194/wes-2025-244-AC1
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The manuscript reports wind‑tunnel tests on a counter‑rotating wind turbine coupled to a double rotational armature generator. An already available BEM/T method is also validated and used together with a differential‑evolution algorithm for optimal pitch and tip speed ratio evaluation.
The topic of the manuscript fits well within the scope of Wind Energy Science and the text clarity and organization if good.