Structural Analysis and Optimization of a Propeller Under Separate Air and Water Operating Conditions Using One-Way Fluid–Structure Coupling

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

My comments are mainly about the need to improve the introduction, provide a more complete and detailed description of the numerical model, report the y+ values, and perform further validation to increase confidence in the numerical results:

In my opinion, the introduction is excessively brief and the citation should be improved. There are only two citations with all the references grouped: three in the first citation [1-3] and seven in the second [4-10].

It is recommended to include the velocity triangle with the Equations (1) to (4).

Equation (2) contains a typo: the r appears as a subscript.

Omega is defined as the product of 2pi and n. While the choice of units is arbitrary, and since Table III reports velocities in m/s, it would be advisable to include the appropriate conversion factor as well.

There is no information on how the BEMT method was implemented nor on which corrections were applied.

Tables 1 and 2 do not explain the meaning of each column.

Figure 1a and 1b show two curves (green and red), but it is not indicated what they represent.

The description of the numerical model is incomplete. The turbulence model is SST k-w and requires appropriate near-wall mesh resolution. For this reason, it is essential to present the y+ parameter in order to determine whether the boundary layer is being properly resolved by the turbulence model.

The numerical model results should be validated before performing the structural analysis.

All figures should be revised. For example:

* Fig. 1: The definition of the pressure coefficient is missing, and the x/c coordinate is not indicated on the axis.
* Fig. 2: Fig.d is missing.
* Fig. 3: Fig.a is missing.

Table IV presents the mesh sensitivity analysis, but the mesh itself has not been shown previously. Additionally, the computational domain dimensions and the boundary conditions employed are not provided.

The method used to enable rotor rotation is not specified. If a sliding-mesh approach was employed, the time-step size should be reported.

To increase confidence in the results, the authors should demonstrate whether a mesh with only 380k cells is capable of accurately predicting the CL and CD at the Reynolds number investigated.

Author Response

Please see the attachment.

 

 

 

   

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript employs BEMT, CFD, and one-way fluid–structure coupling to investigate the structural response and local improvement of a cross-medium impeller. The study has certain engineering significance, but the manuscript still requires revision.

1. The medium, rotational speed, and inflow velocity are changed simultaneously among the three operating conditions, making it difficult to isolate the effect of the medium. It is recommended to further clarify the basis for the operating-condition design and interpret the differences among the conditions cautiously.
2. The current study only simulates the impeller operating entirely in air or water, without considering actual cross-medium processes such as air–water interface crossing. It is recommended to clarify the research scope and revise the title, abstract, and conclusions accordingly.
3. The maximum blade deformation under the water condition reaches 6.11 mm, while the one-way fluid–structure coupling assumption lacks quantitative justification. It is recommended to provide an applicability assessment or further validation.
4. The mesh-independence analysis and numerical model validation remain insufficient. It is recommended to include additional indicators such as thrust or torque, and structural stress, and compare the results with experimental data, or published results.
5. The current “optimization study” is closer to a comparison of limited schemes. Clarify the optimization objectives, variables, and constraints, and provide analyses of the thrust, torque, and efficiency of the final design.
6. Check the manuscript for presentation and formatting issues, including the small fonts and color bars in Figures 3–7, inconsistent terminology and formatting, and the limited number and insufficient relevance of some references.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper entitles "Structural Analysis and Optimization of a Cross-Medium Impeller Based on Fluid-Structure Coupling" focuses on the characteristics of cross-medium propulsion impellers that must operate in both air and water, and investigates their load characteristics under multiple operating conditions, structural responses, and local optimization. The topic is novel and aligns with current interests in flow control, but several aspects require clarification to strengthen the technical rigor and readability.

1. It has been noted that the font styles of some equations, such as Equations (5) and (6), are inconsistent throughout the text. The authors are requested to review the full paper and make the necessary revisions.

2. The legends in Figures 4 and 5 are too small for readers to read clearly. If the legends of the subfigures are the same, it is suggested to display only one larger legend for easier reading.

3. It is noted that the calculation method for the "Score" in Tables I and II is not clearly defined. Details such as the normalization formula and weight distribution are missing and should be provided.

4. It is requested that a brief verification of mesh independence be added to the manuscript.

 

 

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have partially addressed the issues raised in the previous review. In addition, I believe the following comments could improve the overall quality of the manuscript:

It is highly recommended to include the velocity triangle to understand Eq. 1-4.

Eq. 4 contains a typo: “Vs” appears instead of “Va”

Eq. 5 contains “dL” twice.

Regarding Rev.1-5: Assuming you are referring to lines L87–94, that paragraph does not explain anything about how the BEMT method was employed. It only lists its limitations.

Since this study combines BEMT, CFD, and FEM, it would be recommended to compare the forces predicted by each method.

The authors have provided more information on Eq.13-15, but it is difficult to understand the criteria for the weights and what each term in the equations represents.

In Figure 2, it is difficult to appreciate the geometry of the propeller in the computational domain.

In the Figure showing the mesh, it is hard to distinguish anything. At the very least, the authors should include some detail of the mesh on the surfaces of the propeller.

Figure 2 does not show the length of the domain. It is recommended that this be included.

The chord length used in the simulation is unclear. It should be specified so that the domain dimensions are appropriate for the simulation.

Author Response

< fluids >

< Structural Analysis and Optimization of a Cross-Medium Impeller Based on Fluid-Structure Coupling >

Dear Editor,

Thank you for your useful comments and suggestions on our manuscript. We have revised the manuscript accordingly, and detailed corrections are listed below point by point:

Response to review 3:

• It is highly recommended to include the velocity triangle to understand Eq. 1-4.
• Thank you for this valuable suggestion. We agree that a velocity triangle is helpful for clarifying the physical and geometric relationships underlying Eqs. (1)–(4). Accordingly, a new velocity-triangle schematic has been added as Figure 1 in Section 2.1. The figure explicitly illustrates the axial velocity (V_a), tangential velocity (V_t), resultant relative velocity (W), inflow angle (\phi), blade pitch angle (\beta), and angle of attack (\alpha). In addition, the corresponding text has been revised to clarify that (\phi) is defined between the relative velocity (W) and the plane of rotation, and that the local angle of attack is determined from (\alpha=\beta-\phi). These revisions provide a clearer geometric interpretation of Eqs. (1)–(4) and improve the readability of the BEMT formulation. (line 70-88).
• 4 contains a typo: “Vs” appears instead of “Va”
• The corresponding content has been updated. (line 79).
• Regarding Rev.1-5: Assuming you are referring to lines L87–94, that paragraph does not explain anything about how the BEMT method was employed. It only lists its limitations.
• The corresponding content has been updated. (line 70-88).
• Since this study combines BEMT, CFD, and FEM, it would be recommended to compare the forces predicted by each method.
• We agree that comparison among different numerical approaches can be useful for assessing methodological consistency. However, in the present study, BEMT, CFD, and FEM are employed for different purposes and do not independently predict the same force quantities. BEMT is used as a reduced-order method for preliminary propeller screening based on integral thrust, torque, and efficiency, whereas CFD is used to resolve the three-dimensional non-uniform pressure distribution on the blade surfaces. The CFD-derived pressure field, together with the centrifugal load, is subsequently transferred to the FEM model to evaluate structural stress and deformation. Therefore, FEM does not independently predict the hydrodynamic forces, and a direct three-way force comparison among BEMT, CFD, and FEM would not be physically equivalent. In addition, differences between BEMT and CFD are inherently expected because BEMT relies on blade-element and momentum assumptions, while CFD resolves three-dimensional flow effects. For these reasons, we respectfully retain the present methodological framework without adding a direct force comparison.
• The authors have provided more information on Eq.13-15, but it is difficult to understand the criteria for the weights and what each term in the equations represents.
• Equations (14) and (15) are engineering scoring functions used only for relative screening of candidate configurations. The weights of 0.50, 0.35, and 0.15 correspond to efficiency, thrust, and power consumption, respectively. Efficiency receives the highest weight because it best reflects overall propulsive performance, thrust represents the required propulsion capability, and power mainly serves as a constraint. These weights are not universal physical constants but fixed engineering decision parameters applied consistently to all candidates. Therefore, the present formulation is retained.
• In Figure 2, it is difficult to appreciate the geometry of the propeller in the computational domain.
• The corresponding content has been updated. (line 177-182).
• In the Figure showing the mesh, it is hard to distinguish anything. At the very least, the authors should include some detail of the mesh on the surfaces of the propeller.
• The corresponding content has been updated. (line 177-182).
• Figure 2 does not show the length of the domain. It is recommended that this be included.
• The corresponding content has been updated. (line 177-182).
• The chord length used in the simulation is unclear. It should be specified so that the domain dimensions are appropriate for the simulation.
• The corresponding content has been updated. (line 177-182).

 

The manuscript has been resubmitted to your journal. We look forward to your positive response.

Sincerely,

 

 

 

   

Author Response File: Author Response.pdf