A High-Efficient Modeling Method for Aerodynamic Loads of an Airfoil with Active Leading Edge Based on RFA and CFD

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The author developed a new and effective approach that combines the CFD and RAF methods to model the aerodynamic performance of an airfoil with the active leading edge. This study is interesting, but it should address the following comments before publication:

1. Page 1, line 26-27,  "is capable to be" ?  Please reconsider this phase.

2. The frequent use of "And" at the beginning of sentences should be avoided

3. Page 2, lines 81-86: The sentences associated with reference [16] appear out of context in this paragraph. The paragraph introduces the CFD model for the rotor with an active control device, whereas these sentences focus on a combined flow control strategy.

4. Page 3, line 138: CFD is the abbreviation of Computational Fluid Dynamics
5. Page 4, equation (2), what is the time derivative scheme used in the CFD model?

6. Page 4: Provide additional details about the numerical algorithms used in the CFD model, including the spatial and temporal discretization schemes, as well as the turbulence model, preferably in the section introducing the CFD methodology.

7. Page 18: Starting on this page, the model validation section lacks clarity. Specifically, the comparison between CFD results and fitted results remains unclear to me. While some fitted results align well with CFD solutions, others exhibit significant discrepancies. For instance, on page 26, it is evident that the fitted model poorly predicts the lift coefficient (Cl) at high angles of attack, yet the author claims good agreement between these results. Such a claim is inappropriate and should be supported by an error distribution (e.g., in a table or figure) to clarify this discrepancy and improve the validation process. 

 

Comments on the Quality of English Language

The English quality is not good, it should be improved before publication

Author Response

Please find our detailed responses to your comments in the attachment. Thank you.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This research presents a high-efficiency aerodynamic modeling method for an airfoil with an active leading edge using Computational Fluid Dynamics (CFD) and Rational Function Approximation (RFA). The method captures unsteady aerodynamic loads by simulating complex airfoil motions and identifying key model coefficients from CFD data. Validation against CFD results shows strong accuracy and a significant reduction in computational time. The model effectively accounts for varying deflection amplitudes, frequencies, and phases, making it suitable for aeroelastic analysis of rotors with active control devices, particularly for vibration reduction in helicopters.

              This research consists of CFD, Identification, and Load Calculation Processes. The reviewer cannot assess the last two processes, as it is not within my expertise, but can assess only the CFD process. It makes sense. Additionally, the overall results and validation are reasonable. The comments and questions below are helpful to improve the manuscript. Please describe all in the revised manuscript.

• What is the CFD used in this research? Does this software use Eqs. (1)-(2) to calculate the aerodynamic results?
• What is the overlapping meshing method? Why do you use it?
• 2(b) may have a typo.
• The reviewer found that it is very difficult to link lines 223-242 with Fig. 1. Please revise them by focusing on the parameters presented in this Fig. The explanation and the Fig. should be aligned.
• Lines 302-306 need an additional explanation to confirm the agreement between simulation and experimental results in terms of density, Cp, etc. How about them? Why both results are consistent? The current writing is too rough. C- D and E-F seem the same.
• What are the limitations of the aerodynamic model for the airfoil with active leading edge you have developed?
• The maximum discrepancy between the aerodynamic model and CFD results of Fig. 19-21 should be reported.
• From Fig. 19-21, How about the reliability of the aerodynamic model results for amplitude exceeding 3°? Why do you not consider it?
• Also, from Fig. 22-25, How about the reliability of the aerodynamic model results for frequency exceeding 4Hz°? Why do you not consider it?
• The authors should describe the benefits and outcomes of Fig. 19-27 and show examples of their application in your work. These are useful for readers to apply your work further.

Author Response

Please find our detailed responses to your comments in the attachment. Thank you.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The author has addressed most of my comments, but some areas require further explanation as well.

1. The authors often refer to the overlapping grids method without providing relevant details. For example, which overlapping grid method did the authors use, and how did this method deal with donor cells?
2. The author said they used the pressure-based solver for the compressible Navier-Stokes equations in the review letter. How to address the coupling between pressure, density, and velocity.
3. On page 3, line 141, what is the meaning of "m"?
4. On page 4, line 164, what is PRESTO! approach? Please give the full letters, not just the abbreviations.
5. What are the next steps after this study? Do the authors have ideas for improving the model for application in stall areas? Can you discuss this a bit more?

Author Response

Comments 1: The authors often refer to the overlapping grids method without providing relevant details. For example, which overlapping grid method did the authors use, and how did this method deal with donor cells?

Response 1: Thank you for pointing this out. We agree with this comment. The modifications have been added on page 4, lines 164-169. The classic overlapping grid approach with direct hole cutting, which was implemented in ANSYS Fluent, was employed in this study. Faces of cut zones were identified as different types and overlapping cut faces were marked based on adjacent cell sizes and local feature angles. Donor cells were selected based on grid priorities. Cells on overlapping cut faces with highest grid priority were principal donor cells. These cells, along with those connected by faces or nodes, are used as donor candidates.

Comments 2: The author said they used the pressure-based solver for the compressible Navier-Stokes equations in the review letter. How to address the coupling between pressure, density, and velocity.

Response 2: Thank you for your question. In calculations, the coupling among pressure, density, and velocity was handled as follows: The equation of state of ideal gases is employed to establish the relationship among pressure, density, and temperature. For compressible flows, the ideal gas law is written in the following form: where  is the operating pressure,  is the local static pressure relative to the operating pressure,  is the universal gas constant, and  is the molecular weight. The temperature, , will be calculated from the energy equation. The mass flux correction  is added to satisfy the continuity equation. where  ,  are pressure corrections with the two cells on either side of face .  is a function of the average of the momentum equation coefficients . Once a solution is obtained, the cell pressure  and the face flux  are corrected using Here  and  are a guesses pressure field and resulting face flux respectively from the momentum equation.  is the cell pressure correction,  is the under-relaxation factor for pressure. The corrected face flux, , satisfies the discrete continuity equation identically during each iteration.

Comments 3: On page 3, line 141, what is the meaning of "m"?

Response 3: Thank you for pointing this out. The phrase “the m” has been modified to “this approach” on page 3, line 141.

Comments 4: On page 4, line 164, what is PRESTO! approach? Please give the full letters, not just the abbreviations.

Response 4: Thank you for pointing this out. The phrase “PRESTO!” in Figure 2(b) has been modified to “PRESTO! (PREssure STaggering Option) scheme” on page 4, line 164. PRESTO! is a pressure interpolation scheme, which is used to compute the face pressure of a control volume with the discrete continuity balance. More details can be found on page 701 of ANSYS Fluent Theory Guide (Release 19.0). With this scheme, independent control volumes are employed and pressure gradient variations can be calculated accurately. PRESTO! is applicable to structured and unstructured grids, which can be used in cases in this study.

Comments 5: What are the next steps after this study? Do the authors have ideas for improving the model for application in stall areas? Can you discuss this a bit more?

Response 5: Thank you for your question. An aeroelastic model can be developed with the modeling method to investigate aeroelastic response of active rotor with active leading edges in the next step. The developed model in this study can be improved through the following two aspects: a). The RFA model applied in this study is based on linear or quasi-linear assumptions. Nonlinearity of RFA model can be improved with series expansion, which may be helpful for predicting nonlinear effects of airfoil in stall aeras. b). CFD method may lead to errors in calculations due to turbulent model, boundary conditions and solver settings. Wind tunnel experimental data can be used to improve the reliability of aerodynamic data employed for identification.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript has been revised based on my suggestions and comments, and it is now suitable for publication.

Author Response

Thank you.

Author Response File: Author Response.docx