A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling

Round 1

Reviewer 1 Report

This paper deals with the optimal design of a flight vehicle using only mesh data that forms the shape of area rules in the transonic region.

It is a significant achievement because it shows the possibility of achieving optimization equivalent to CFD calculation results at an overwhelmingly low cost, without using CFD calculations.

In this research, it is essential to reproduce cross-sectional area changes from shape data with high accuracy, which is carefully explained.

The effectiveness of this method has been applied to spherical and other shapes, and the results are well-studied and effective.

One comment I would make is to consider the lattice length of the surface.

In the case of the sphere, an average lattice length of 0.05 m was applied for a radius of 1 m. What would be the result if this size were changed?

Also, in the case of the actual vehicle geometry, I think applying a finer grid length in places where the geometry changes locally is necessary. Please show the results of your study in this area.

The followings are minor typo.

Line 241 rad ?

Ref.11 The authors names are missing.

Author Response

The authors would like to thank reviewer 1 for their detailed analysis of the paper.  In response to each of the comments made:

• In the case of the sphere, an average lattice length of 0.05 m was applied for a radius of 1 m. What would be the result if this size were changed?Some additional comments have been made within sub-section 3.3.1 to clarify why this cell size was chosen with a some discussion around the likely impact of cell size.  Running a further mesh resolution dependency study was deemed beyond the scope of what was possible in the time available to provide the manuscript revision.  Note that this paper simply aims to prove the point that this 'area ruling' based approach works in principle. In the revised manuscript we provide an additional recommendation that if this is to be used in by others for real applications then mesh dependency studies should be carried out (as you would normally in a CFD-based approach).
• Also, in the case of the actual vehicle geometry, I think applying a finer grid length in places where the geometry changes locally is necessary.

As above, in the time available to provide a revised manuscript this was not possible but this has now been addressed in the conclusions and recommendations.

• Two minor typos

These have both been corrected in the revised manuscript.

Reviewer 2 Report

Dear authors,

This paper presents a mesh-based, CFD-free wave drag estimation method and shows aerodynamic optimization utilizing this method. The paper is well-structured and the figures are clear. I only have very few questions/comments:

1) general question: maybe I overlooked something, but it seems that you calculate the wave drag by using transonic area rule. I am curious that why it needs to be "mesh-based"? I mean one can also cut the 3D model by just using CAD software/tools.

2) The introduction section is too simplified. Some more background introduction of the "state-of-the-art" and "existing gaps" in this field is nessary for readers' motivation.

Author Response

The authors would like to thank reviewer 2 for their feedback on the paper.  In response to the two comments made:

1) general question: maybe I overlooked something, but it seems that you calculate the wave drag by using transonic area rule. I am curious that why it needs to be "mesh-based"? I mean one can also cut the 3D model by just using CAD software/tools.

We acknowledge that this might have been unclear in the original version.  Additional content within the introduction now directly addresses this point.

 2) The introduction section is too simplified. Some more background introduction of the "state-of-the-art" and "existing gaps" in this field is nessary for readers' motivation.

The introduction has been expanded (including the addition of 5 new references) to summarise the state of the art and strengthen the motivation for exploring the approach outlined in the paper (especially with regards to comment 1).

Round 2

Reviewer 1 Report

The reply is sufficient and the revised article is worth for publication.