the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 May 2022
A New Way to Estimate Maximum Power from Wind Turbines: Linking Newtonian with Action Mechanics
Abstract. A more accurate way to calculate power output from wind turbines based on fundamental Newtonian mechanics is proposed for testing. This contrasts with current methods regarded as governed by flows of kinetic energy through an area swept by rotating airfoils. Action mechanics measures torques caused by conservation of momentum of impulsive air streams on rotor surfaces at differing radii. We integrate the windward torque using inputs of rotor dimensions, the angle of incidence and strength of wind impulses on the blade surfaces. A reverse torque in the plane of rotation is estimated as radial impulses from the blade’s rotation. Net torque is converted to power by the angular velocity of the turbine rotors. A matter of concern is significant heat production by wind turbines, partly from leeward reactions but mainly from turbulent release of vortical energy. Use of wind farms as sources of renewable energy may need better practice, minimizing environmental impacts guided by this hypothesis.
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RC1: 'Comment on wes-2022-22', Anonymous Referee #1, 11 May 2022
This manuscript contains sentences like “The air particles impact on trajectories imposing the inertia of the wind velocity on their far greater microscopic velocities, with mean free paths of the order of picometers” from which it can be judged as poorly written and lacking in a fundamental understanding of fluid mechanics. Fundamental to the subject, and to the analysis of wind and hydrokinetic turbines in particular, is the continuum hypothesis. Fluids are, effectively, infinitely divisible, and thus describable by partial differential equations. The molecular dynamics of the fluid are important only in setting the viscosity and other fluid properties. As with many fundamental issues, the continuum hypothesis is thoroughly described and justified in Batchelor (1967, Section 1.2). It follows that results such as the Betz-Joukovsky limit on power output apply equally to wind and hydrokinetic turbines despite the huge differences in the molecular structure of the two fluids. Further, any discussion of the generation of power that relies on the consideration of molecular or microscopic behaviour is pointless. In the context of conventional fluid dynamics, Equation (3) in the manuscript is irrelevant to power production and Equation (4) appears to be a crude approximation to the conventional blade element lift and drag formulations. It is not possible to comment further because no derivation of the equation is given. Equation (6) is incorrect because it equates extracted to output power and so ignores the efficiencies of the drivetrain, generator, and power electronics.
This is the first wind energy manuscript I have reviewed that mentions the philosopher Karl Popper and his ideas of falsificationism as the delineation between scientific and nonscientific knowledge. These ideas were discredited years ago – as an example of the trap of falsifiability: I make the falsifiable prediction that Vladimir Putin will die tomorrow. Is this a scientific hypothesis? No. Nevertheless, Popper would, I think, also recommend that this manuscript be rejected as it contains no testable or even tested results. In summary, the manuscript comprises an incorrect and largely irrelevant and useless analysis that makes no contribution to the scientific literature on wind turbines.
Additional Reference
G.K. Batchelor (1967), An Introduction to Fluid Dynamics, C.U.P.
Citation: https://doi.org/10.5194/wes-2022-22-RC1 -
AC1: 'Reply on RC1', Ivan Kennedy, 13 May 2022
We thank Reviewer 1 for critical discussion given in response to our article. From these comments, we can make certain improvements.
However, it seems unfair to review our article using an approach based purely on continuum calculus rather than the “new way” we propose based on wind momentum and blade pressures. The reviewer inflexibly prefers the “old way” even though it has many uncertainties that this article seeks to solve. Partial differential equations typify continuum hypothesis, even though air in wind is not infinitely divisible but consists of particles exerting pressure with momentum and direction. We request that the review be conducted fairly, by considering instead the Newtonian experimental mechanics conserving momentum that we base our method on. The new action mechanics explains the close to cubic response of maximum power to wind speed but raises issues with respect to angle of attack and blade length that need more investigation. The review should not be about mathematical purism, particularly when the extensive results found with this new method are more accurate than current approaches based more loosely on the wind’s kinetic energy.
- Our title indicates we only intended to estimate maximum theoretical power from wind turbines, a function of wind speed and the angle of the blade with respect to the wind. We consider this a very useful result. Our equations were never intended to deal with inefficiencies in the drive train and electrical equipment. We claim therefore that equation (6) is true in terms of the title of the article.
- We were careful to explain that only the relatively small directional wind vector existing over the random microscopic velocities was relevant. We never discussed generation of power from molecular or microscopic behaviour as claimed, except in terms of the rate of radial action of particles moving in wind, that we define as torques.
- We consider that section 1.1 Radial action theory and Figure 1 adequately explain the derivation of equations (4) and (5), in terms of moments generated by wind pressure and the blades on air, controlled by tip-speed ratio. However, we will improve this text for logical clarity.
- We make clear that drag as normally understood for aerofoils does not apply for estimating the leeward or back torque of equation (5). Given the much greater velocity of most of the turbine blade impacting air up to the tip compared to wind speed, while lift is important drag is irrelevant.
- Regarding experimental testing of our hypothesis, Figure 3 illustrates one obvious test in its prediction of an optimum angle for flat blades near 55-60 degrees or wind incidence. Another critical test in the spirit of Karl Popper’s definition of rich hypotheses relates to the existence of an optimum blade length. Ultimately the tip-speed ratio of longer blades defeats the windward torque depending on wind speed. Responding to the criticism regarding possible falsification, we will now include differential equations for variations in power with respect to angle of wind incidence ∂P/∂θ, blade length ∂P/∂L varying with wind speed and optimum length with wind speed, all predictions testable in field practice.
Unfortunately, Reviewer 1 only considered the first few pages of our article, neglecting completely the equally novel hypothesis regarding heat generation, based firmly on our three recent publications in the Entropy journal. This prediction is also eminently testable and is confirmed in some respects in recent papers in other journals. Given the utility of our simple equations for estimating maximum wind power and their correspondence to the demonstrated power of real-world turbines, we reject the reviewer’s final sentence as unscientific and as unhelpful as the comment on predicting Putin’s future.
Citation: https://doi.org/10.5194/wes-2022-22-AC1
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AC1: 'Reply on RC1', Ivan Kennedy, 13 May 2022
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AC2: 'Comment on wes-2022-22', Ivan Kennedy, 21 Jun 2022
The attached Python file may be of interest to the Community. Previous code was included in the Supplementary Material as a Python Notebook. Some may prefer the code in Python, as supplied by coauthorNikolas Crossan. Note that this code is based on estimating turbine power from the difference in the windward and leeward torques, according to the tip-speed ratio and was used to Figure 4 in the article.
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RC2: 'Comment on wes-2022-22', Anonymous Referee #2, 15 Jul 2022
After reviewing the manuscript “A New Way to Estimate Maximum Power from Wind Turbines: Linking Newtonian with Action Mechanics” by Kennedy et al., I came to the conclusion that it is not just poorly written but also does not adhere to the standards expected of a scientific paper. These deficits make the evaluation of the ideas presented considerably more difficult. For this reason, I recommend a rejection of the manuscript at this stage.
More specific comments (in the order of their appearance in the manuscript):
ll 16-25: The abstract is far from sufficiently specific. Statements as with the last sentence are rather inappropriate and should be replaced by more specific conclusion and summarized results.
ll 28: The introduction includes far too few references, so that most statements and given details are not sufficiently verified.
ll 57: The introduction of “action mechanics” and explanation what is meant by it, comes far too late here.
l 73: Somewhere there should be an introduction of the manuscripts structure – maybe here.
l 80 (e.g.): It is not clear to me why the authors use square brackets here. Overall, inclusion of maths should be reviewed and revised carefully.
l 87: Both Figure 1 and 2 are far too busy and must be revised and improved.
ll 93: The authors follow a very unconventional structure (for this type of scientific publications) – in particular this part does not seem suitable for being part of (still) the introduction.
l 172: Formatting of equations (not just this one) needs to revised and improved.
l 184: Please use section numbers for referencing instead.
l 189: Nice to read this but not suitable for a scientific paper.
l 239: Also, having a “Methods” section after the “Results” is not common and does not support a well structured manuscript.
l 253: All the details summarized in the table lack suitable references.
l 298: Bad figure quality.
Citation: https://doi.org/10.5194/wes-2022-22-RC2 -
AC3: 'Reply on RC2', Ivan Kennedy, 19 Jul 2022
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2022-22/wes-2022-22-AC3-supplement.pdf
-
AC3: 'Reply on RC2', Ivan Kennedy, 19 Jul 2022
Status: closed
-
RC1: 'Comment on wes-2022-22', Anonymous Referee #1, 11 May 2022
This manuscript contains sentences like “The air particles impact on trajectories imposing the inertia of the wind velocity on their far greater microscopic velocities, with mean free paths of the order of picometers” from which it can be judged as poorly written and lacking in a fundamental understanding of fluid mechanics. Fundamental to the subject, and to the analysis of wind and hydrokinetic turbines in particular, is the continuum hypothesis. Fluids are, effectively, infinitely divisible, and thus describable by partial differential equations. The molecular dynamics of the fluid are important only in setting the viscosity and other fluid properties. As with many fundamental issues, the continuum hypothesis is thoroughly described and justified in Batchelor (1967, Section 1.2). It follows that results such as the Betz-Joukovsky limit on power output apply equally to wind and hydrokinetic turbines despite the huge differences in the molecular structure of the two fluids. Further, any discussion of the generation of power that relies on the consideration of molecular or microscopic behaviour is pointless. In the context of conventional fluid dynamics, Equation (3) in the manuscript is irrelevant to power production and Equation (4) appears to be a crude approximation to the conventional blade element lift and drag formulations. It is not possible to comment further because no derivation of the equation is given. Equation (6) is incorrect because it equates extracted to output power and so ignores the efficiencies of the drivetrain, generator, and power electronics.
This is the first wind energy manuscript I have reviewed that mentions the philosopher Karl Popper and his ideas of falsificationism as the delineation between scientific and nonscientific knowledge. These ideas were discredited years ago – as an example of the trap of falsifiability: I make the falsifiable prediction that Vladimir Putin will die tomorrow. Is this a scientific hypothesis? No. Nevertheless, Popper would, I think, also recommend that this manuscript be rejected as it contains no testable or even tested results. In summary, the manuscript comprises an incorrect and largely irrelevant and useless analysis that makes no contribution to the scientific literature on wind turbines.
Additional Reference
G.K. Batchelor (1967), An Introduction to Fluid Dynamics, C.U.P.
Citation: https://doi.org/10.5194/wes-2022-22-RC1 -
AC1: 'Reply on RC1', Ivan Kennedy, 13 May 2022
We thank Reviewer 1 for critical discussion given in response to our article. From these comments, we can make certain improvements.
However, it seems unfair to review our article using an approach based purely on continuum calculus rather than the “new way” we propose based on wind momentum and blade pressures. The reviewer inflexibly prefers the “old way” even though it has many uncertainties that this article seeks to solve. Partial differential equations typify continuum hypothesis, even though air in wind is not infinitely divisible but consists of particles exerting pressure with momentum and direction. We request that the review be conducted fairly, by considering instead the Newtonian experimental mechanics conserving momentum that we base our method on. The new action mechanics explains the close to cubic response of maximum power to wind speed but raises issues with respect to angle of attack and blade length that need more investigation. The review should not be about mathematical purism, particularly when the extensive results found with this new method are more accurate than current approaches based more loosely on the wind’s kinetic energy.
- Our title indicates we only intended to estimate maximum theoretical power from wind turbines, a function of wind speed and the angle of the blade with respect to the wind. We consider this a very useful result. Our equations were never intended to deal with inefficiencies in the drive train and electrical equipment. We claim therefore that equation (6) is true in terms of the title of the article.
- We were careful to explain that only the relatively small directional wind vector existing over the random microscopic velocities was relevant. We never discussed generation of power from molecular or microscopic behaviour as claimed, except in terms of the rate of radial action of particles moving in wind, that we define as torques.
- We consider that section 1.1 Radial action theory and Figure 1 adequately explain the derivation of equations (4) and (5), in terms of moments generated by wind pressure and the blades on air, controlled by tip-speed ratio. However, we will improve this text for logical clarity.
- We make clear that drag as normally understood for aerofoils does not apply for estimating the leeward or back torque of equation (5). Given the much greater velocity of most of the turbine blade impacting air up to the tip compared to wind speed, while lift is important drag is irrelevant.
- Regarding experimental testing of our hypothesis, Figure 3 illustrates one obvious test in its prediction of an optimum angle for flat blades near 55-60 degrees or wind incidence. Another critical test in the spirit of Karl Popper’s definition of rich hypotheses relates to the existence of an optimum blade length. Ultimately the tip-speed ratio of longer blades defeats the windward torque depending on wind speed. Responding to the criticism regarding possible falsification, we will now include differential equations for variations in power with respect to angle of wind incidence ∂P/∂θ, blade length ∂P/∂L varying with wind speed and optimum length with wind speed, all predictions testable in field practice.
Unfortunately, Reviewer 1 only considered the first few pages of our article, neglecting completely the equally novel hypothesis regarding heat generation, based firmly on our three recent publications in the Entropy journal. This prediction is also eminently testable and is confirmed in some respects in recent papers in other journals. Given the utility of our simple equations for estimating maximum wind power and their correspondence to the demonstrated power of real-world turbines, we reject the reviewer’s final sentence as unscientific and as unhelpful as the comment on predicting Putin’s future.
Citation: https://doi.org/10.5194/wes-2022-22-AC1
-
AC1: 'Reply on RC1', Ivan Kennedy, 13 May 2022
-
AC2: 'Comment on wes-2022-22', Ivan Kennedy, 21 Jun 2022
The attached Python file may be of interest to the Community. Previous code was included in the Supplementary Material as a Python Notebook. Some may prefer the code in Python, as supplied by coauthorNikolas Crossan. Note that this code is based on estimating turbine power from the difference in the windward and leeward torques, according to the tip-speed ratio and was used to Figure 4 in the article.
-
RC2: 'Comment on wes-2022-22', Anonymous Referee #2, 15 Jul 2022
After reviewing the manuscript “A New Way to Estimate Maximum Power from Wind Turbines: Linking Newtonian with Action Mechanics” by Kennedy et al., I came to the conclusion that it is not just poorly written but also does not adhere to the standards expected of a scientific paper. These deficits make the evaluation of the ideas presented considerably more difficult. For this reason, I recommend a rejection of the manuscript at this stage.
More specific comments (in the order of their appearance in the manuscript):
ll 16-25: The abstract is far from sufficiently specific. Statements as with the last sentence are rather inappropriate and should be replaced by more specific conclusion and summarized results.
ll 28: The introduction includes far too few references, so that most statements and given details are not sufficiently verified.
ll 57: The introduction of “action mechanics” and explanation what is meant by it, comes far too late here.
l 73: Somewhere there should be an introduction of the manuscripts structure – maybe here.
l 80 (e.g.): It is not clear to me why the authors use square brackets here. Overall, inclusion of maths should be reviewed and revised carefully.
l 87: Both Figure 1 and 2 are far too busy and must be revised and improved.
ll 93: The authors follow a very unconventional structure (for this type of scientific publications) – in particular this part does not seem suitable for being part of (still) the introduction.
l 172: Formatting of equations (not just this one) needs to revised and improved.
l 184: Please use section numbers for referencing instead.
l 189: Nice to read this but not suitable for a scientific paper.
l 239: Also, having a “Methods” section after the “Results” is not common and does not support a well structured manuscript.
l 253: All the details summarized in the table lack suitable references.
l 298: Bad figure quality.
Citation: https://doi.org/10.5194/wes-2022-22-RC2 -
AC3: 'Reply on RC2', Ivan Kennedy, 19 Jul 2022
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2022-22/wes-2022-22-AC3-supplement.pdf
-
AC3: 'Reply on RC2', Ivan Kennedy, 19 Jul 2022
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