the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 May 2024
Velocity correction for the Actuator Line Method
Abstract. We introduce a velocity correction designed to mitigate the overestimation of aerodynamic loads observed with the traditional Actuator Line Method (ALM) at the blades tip. The correction is based on Blade Element Momentum (BEM) theory to determine the ratio of tip-corrected to non-tip-corrected axial and tangential velocity components. These velocity ratios are used to correct the velocities at the blade locations, ensuring an accurate representation of aerodynamic effects near the blade tips. The correction only requires the Tip Speed Ratio (TSR), which can be estimated from local flow conditions and turbine specifications. This makes the method highly adaptable to various flow scenarios. The effectiveness of the proposed correction has been validated through Large Eddy Simulations (LES) at multiple inflow velocities through comparison against both BEM with tip correction and a vortex-based smearing correction for ALM.
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Status: closed
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RC1: 'Comment on wes-2024-60', Anonymous Referee #1, 21 Jun 2024
The authors are presenting a BEM-based velocity correction to the ALM. The AL velocities are scaled with the ratio of BEM induction with tip correction to BEM without tip correction. The paper defines the method with some minor shortcomings, however the method is in itself flawed. The authors seem to be unaware of nowadays well-established AL theory (multiple papers from different research groups), that the vortex-core smearing originating from the force distribution kernel, leads to missing some induction at the blade. The ALM thus needs a vortex-core or smearing correction that computes the missing induction, not a tip correction. The effect of the BEM tip correction on the blades' induction only behaves similarly to the one by the AL vortex-core smearing correction, as they both are related to the trailed vorticity. ALM simulations do not entirely lack the induction from the trailed vorticity, which BEM tip corrections correct for, but only a part of it in the core of the trailed vorticies due to force smearing. Medium-fidelity aeroelastic solvers actually use BEM together with vortex corrections instead of tip corrections. The authors also need to argue why it is beneficial to move to their proposed correction if other fast methods are already available. In terms of each flow solver iteration the cost of the AL correction is usually negligible.
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RC2: 'Comment on wes-2024-60', Anonymous Referee #2, 10 Jul 2024
The manuscript presents a novel correction for the actuator line method that is commonly used in numerical simulations of wind turbines and farms. The proposed correction accounts for the change in velocity near the blade tips due to three-dimensional effects and does so by solving a BEM algorithm with tip velocity correction within the ALM correction algorithm. According to the authors, this approach is faster and more versatile than existing ALM tip corrections and it is shown to yield satisfactory results when compared to another tip correction algorithm as well as the original BEM algorithm with tip velocity correction, which it aims to reproduce.The manuscript is well written and clearly structured. It explains the current state of the literature, introduces the novel correction method and provides validation of the method. I recommend the manuscript for publication. Below are some minor comments:
- I am not sure that all the plots are necessary, as they often show very similar things. Potentially some could be combined.
- fig. 1: Typing error in the legend.
- line 81f: What are the tip speed ratio and the Reynolds number for these conditions? At least the Reynolds number could be stated later in line 156.
- line 125ff: This text repeats what is shown in figure 4. Can they be combined?
- line 165: Why was the grid spacing of 2m used for the validation?
- line 173: Typing error
- section 6.4: Can you comment on why the results would be sensitive to inflow velocity? Can you convert the inflow velocities to Reynolds numbers?
- line 226ff: The title of the appendix needs editing. Also, what is the purpose of the appendix? Can you elaborate on this?
Citation: https://doi.org/10.5194/wes-2024-60-RC2 -
RC3: 'Comment on wes-2024-60', Anonymous Referee #3, 11 Jul 2024
This paper presents a tip correction implementation in the actuator line model. The method calculates the scaling between the velocity from BEM with a tip correction and without a tip correction. The scaling is used to modify the velocity sampled in the ALM. The authors have obtained results that mimic the behavior of a tip correction in the ALM, as expected.
Unfortunately, the correction is not general and there is no mathematical foundation to support it. I recommend the authors to read the literature in this space to better understand the challenges and contributions that have already been published.
The filtered lifting line theory, and vortex-smearing correction have already solved the problems that these authors pose in a more mathematically consistent and general way. So, the methods that the authors are using do not offer any advantages or improvements to the methods already published in the literature.
The vortex-based smearing correction is a consistent correction for the ALM, and the authors have already implemented it in their code. I recommend the authors to use that correction in future work, as opposed to the correction in this manuscript.
Specific comments:
- “Figure 3 presents a comparison of the axial velocity and angle of attack as obtained from ALM simulations with various grid resolutions with BEM theory. The figure illustrates that the ALM results converge towards BEM theory without tip correction.”
The results don’t look like they are converging to the same BEM solution. Results are dependent on grid resolution and epsilon and this relation has been studied in the literature. The solutions are epsilon dependent.
- “Given the classic ALM convergence to BEM without tip correction, we employ BEM to calculate the ratio between the tip-corrected and sampled velocity.”
This approach is not correct. The classic ALM does not converge towards the BEM solution without a tip correction.
- “Figure 5a demonstrates that the proposed method converges towards BEM theory with tip corrections.”
It does not. Adding a tip correction will make it have a similar behavior near the tip. But the agreement is not good, especially throughout the rest of the blade away from the tip.
- “Moreover, both the normal and tangential loads converge towards those predicted by BEM with tip correction. There are small differences between BEM and ALM within the mid-blade region, originating from the different assumptions in BEM and ALM.”
This observation is correct. The differences between the methods are what creates the differences in results. The literature in this topic has established this understanding well and other approaches that are more consistent have been developed to minimize the differences between the methods.
- “Considering that the ratio of tip-corrected to non-tip-corrected velocities approaches to 1 in the mid-blade region, this does not affect the effectiveness of the proposed method.”
Yes, this is the definition of the tip correction.
- Figure 8 shows that the vortex smearing correction is better at correcting the ALM results.
Citation: https://doi.org/10.5194/wes-2024-60-RC3 - “Figure 3 presents a comparison of the axial velocity and angle of attack as obtained from ALM simulations with various grid resolutions with BEM theory. The figure illustrates that the ALM results converge towards BEM theory without tip correction.”
Status: closed
-
RC1: 'Comment on wes-2024-60', Anonymous Referee #1, 21 Jun 2024
The authors are presenting a BEM-based velocity correction to the ALM. The AL velocities are scaled with the ratio of BEM induction with tip correction to BEM without tip correction. The paper defines the method with some minor shortcomings, however the method is in itself flawed. The authors seem to be unaware of nowadays well-established AL theory (multiple papers from different research groups), that the vortex-core smearing originating from the force distribution kernel, leads to missing some induction at the blade. The ALM thus needs a vortex-core or smearing correction that computes the missing induction, not a tip correction. The effect of the BEM tip correction on the blades' induction only behaves similarly to the one by the AL vortex-core smearing correction, as they both are related to the trailed vorticity. ALM simulations do not entirely lack the induction from the trailed vorticity, which BEM tip corrections correct for, but only a part of it in the core of the trailed vorticies due to force smearing. Medium-fidelity aeroelastic solvers actually use BEM together with vortex corrections instead of tip corrections. The authors also need to argue why it is beneficial to move to their proposed correction if other fast methods are already available. In terms of each flow solver iteration the cost of the AL correction is usually negligible.
-
RC2: 'Comment on wes-2024-60', Anonymous Referee #2, 10 Jul 2024
The manuscript presents a novel correction for the actuator line method that is commonly used in numerical simulations of wind turbines and farms. The proposed correction accounts for the change in velocity near the blade tips due to three-dimensional effects and does so by solving a BEM algorithm with tip velocity correction within the ALM correction algorithm. According to the authors, this approach is faster and more versatile than existing ALM tip corrections and it is shown to yield satisfactory results when compared to another tip correction algorithm as well as the original BEM algorithm with tip velocity correction, which it aims to reproduce.The manuscript is well written and clearly structured. It explains the current state of the literature, introduces the novel correction method and provides validation of the method. I recommend the manuscript for publication. Below are some minor comments:
- I am not sure that all the plots are necessary, as they often show very similar things. Potentially some could be combined.
- fig. 1: Typing error in the legend.
- line 81f: What are the tip speed ratio and the Reynolds number for these conditions? At least the Reynolds number could be stated later in line 156.
- line 125ff: This text repeats what is shown in figure 4. Can they be combined?
- line 165: Why was the grid spacing of 2m used for the validation?
- line 173: Typing error
- section 6.4: Can you comment on why the results would be sensitive to inflow velocity? Can you convert the inflow velocities to Reynolds numbers?
- line 226ff: The title of the appendix needs editing. Also, what is the purpose of the appendix? Can you elaborate on this?
Citation: https://doi.org/10.5194/wes-2024-60-RC2 -
RC3: 'Comment on wes-2024-60', Anonymous Referee #3, 11 Jul 2024
This paper presents a tip correction implementation in the actuator line model. The method calculates the scaling between the velocity from BEM with a tip correction and without a tip correction. The scaling is used to modify the velocity sampled in the ALM. The authors have obtained results that mimic the behavior of a tip correction in the ALM, as expected.
Unfortunately, the correction is not general and there is no mathematical foundation to support it. I recommend the authors to read the literature in this space to better understand the challenges and contributions that have already been published.
The filtered lifting line theory, and vortex-smearing correction have already solved the problems that these authors pose in a more mathematically consistent and general way. So, the methods that the authors are using do not offer any advantages or improvements to the methods already published in the literature.
The vortex-based smearing correction is a consistent correction for the ALM, and the authors have already implemented it in their code. I recommend the authors to use that correction in future work, as opposed to the correction in this manuscript.
Specific comments:
- “Figure 3 presents a comparison of the axial velocity and angle of attack as obtained from ALM simulations with various grid resolutions with BEM theory. The figure illustrates that the ALM results converge towards BEM theory without tip correction.”
The results don’t look like they are converging to the same BEM solution. Results are dependent on grid resolution and epsilon and this relation has been studied in the literature. The solutions are epsilon dependent.
- “Given the classic ALM convergence to BEM without tip correction, we employ BEM to calculate the ratio between the tip-corrected and sampled velocity.”
This approach is not correct. The classic ALM does not converge towards the BEM solution without a tip correction.
- “Figure 5a demonstrates that the proposed method converges towards BEM theory with tip corrections.”
It does not. Adding a tip correction will make it have a similar behavior near the tip. But the agreement is not good, especially throughout the rest of the blade away from the tip.
- “Moreover, both the normal and tangential loads converge towards those predicted by BEM with tip correction. There are small differences between BEM and ALM within the mid-blade region, originating from the different assumptions in BEM and ALM.”
This observation is correct. The differences between the methods are what creates the differences in results. The literature in this topic has established this understanding well and other approaches that are more consistent have been developed to minimize the differences between the methods.
- “Considering that the ratio of tip-corrected to non-tip-corrected velocities approaches to 1 in the mid-blade region, this does not affect the effectiveness of the proposed method.”
Yes, this is the definition of the tip correction.
- Figure 8 shows that the vortex smearing correction is better at correcting the ALM results.
Citation: https://doi.org/10.5194/wes-2024-60-RC3 - “Figure 3 presents a comparison of the axial velocity and angle of attack as obtained from ALM simulations with various grid resolutions with BEM theory. The figure illustrates that the ALM results converge towards BEM theory without tip correction.”
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