Aerodynamic Modeling of a Flying Wing Featuring Ludwig Prandtl’s Bell Spanload

Round 1

Reviewer 1 Report

In general, I am not convinced that the proverse yaw effect (which is certainly there for a bell-type lift distribution) is of predominant interest in the design of a flying wing aircraft. The theory part on VL methods is, in my opinion, not necessary as these methods are well known since a long time. It would have been interesting to attempt an explanation for the discrepancy in the prediction of lift distribution in the inner wing sections between the two methods.

Comments for author File: Comments.pdf

There are a few typos and small language errors. A copy of the pdf with my markups is attached. 

Author Response

Please see attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper addresses the "bell spanload" characteristics associated with "proverse yaw" tendency related to flying wing vehicles.

As the authors state themselves this topic has been thoroughly investigated in the past also including CFD approaches. Nevertheless, some limited further information can be drawn from the paper at hand.

 

The following points should be considered prior to publication:

1) Introduction: The following reference provides a comprehensive overview on the topic contaning also a bulk list of references.

Estela Bragado-Aldana, Mudassir Lone, Atif Riaz: On wings with non-elliptic lift distributions, ICAS Paper 2020-0253, 32nd ICAS Congress, Shanghai, 2020.

2) Geometry and design point:

Major information is missing on the wing and airfoil geometry which is the main drawback of this paper.

(i) While there is a sketch on the wing (dimensions in ft, m would be preferred,  Fig. 1) the dominating non-dimensional parameters, i.e. aspect ratio, taper ratio and sweep (referring to the quarter-line not the leading-edge) are missing. Those data should be explicitely mentioned for the cases investigated, a table would be preferred. A reasoning for the chosen initial values should be provided.

(i) No geometrical data are explicitely attributed to the airfoil geometry (Figs. 3, 4 show the mesh approach), i.e. max. thickness, pos. of max. thickn., max. camber, pos. of max. camber, leading-edge radius, etc. The airfoil geometry has to be defined in detail with respect to the CFD simulations and viscous effects.

(iii) A reasoning for the (design, cruise flight) lift coefficient of 0.6 is not given. This value should be associated with the necessary background information.

3) Results:

The spanwise CFD related distributions providing "dark grey" areas are not very clear ("bar type sequence"). A line distribution as given for the VLM is expected while variations can be highlighted by a certain overlay band.

4) The last section "Discussion" should be entitled "Conclusions". 

No references to Figs. should be made there as the conclusion stands for itself. 

Overall, some parts of the paper can be presented in a more concise and condensed manner.

Some final checks on typos and grammar should be performed.

 

 

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

This paper presents the aerodynamic modeling of a flying wing featuring Ludwig Prandtl’s Bell Spanload. The aerodynamic models are developed using a medium-fidelity vortex lattice method and RANS computational fluid dynamics solution across a wide range of in-flow angle conditions. A methodology is developed to directly compare the spanwise force distributions from each method. The proverse yaw, caused by the twist distribution necessary to produce the Bell Spanload, is calculated in the high and low-order analysis. This research appears to be novel in its approach to comparing medium- and high-fidelity approaches to predicting the proverse yaw feature of the Bell span load.

1. Title: The title should be revised to accurately reflect the content of the paper. Instead of "aerodynamic modeling of an aircraft," it should be changed to "aerodynamic modeling of a flying wing featuring Ludwig Prandtl's Bell Spanload" to align with the terminology used throughout the paper and to provide a more detailed description of the research.

2. Literature background: The authors should ensure they have covered all relevant literature in the field. It is important to include important and similar papers, like some similar papers published in the AIAA SciTech Forum or the Journal of Aircraft. The authors should also provide a more comprehensive discussion of previous research on proverse yaw, addressing any gaps in the existing literature.

Additionally, the authors should incorporate references to papers that explore predictions of vortex lattice methods (VLM) and computational fluid dynamics (CFD) for flying wings, as they mentioned that such predictions are limited but did not cite any related studies. For example, the paper titled "Examination of Proverse Yaw in Bell-Shaped Spanload Aircraft" by Richter, Hainline, and Agarwal (2019) should be included as a relevant citation.

3. Contribution: The authors should clarify and consolidate their statements regarding the scientific contribution of the paper. It is advisable to focus on the specific and unique feature of the Bell span load, which is the proverse yaw, and emphasize the comparison of fidelity between medium-fidelity vortex lattice methods and high-fidelity computational fluid dynamics solvers in predicting this feature. This comparison can be considered the main novelty of the research.

4. Modeling: The authors should accurately represent their modeling approach. While they initially mention solving the full Navier-Stokes equations, they later clarified that they are using Reynolds-averaged Navier-Stokes (RANS) equations, as stated in line 184. This clarification should have been made earlier to avoid confusion.

Furthermore, the authors should include a mesh representation of the complete aircraft in the CFD analysis, in addition to the mesh in the symmetry plane, to provide a more comprehensive visualization of their modeling approach.

The authors should consider including a nonviscous CFD solution, such as the Euler solution, in addition to the RANS solution, to provide a more comprehensive analysis. Comparing the results obtained from both approaches would enhance the completeness of the research and provide better insights into the impact of viscosity on the predicted aerodynamic characteristics.

In the section discussing span load comparison (2.5.1 subchapter), the authors should include a figure illustrating the wing planform discretization or explicitly state the number of panels in the chordwise and spanwise directions. This inclusion would enhance the clarity and completeness of the paper.

Figures of Cp distribution for both CFD and VLM methods should be incorporated to provide a visual representation of the results.

The authors should mention the specific airfoils used and provide a justification for choosing a lift coefficient (CL) value of 0.6 to enhance the transparency of their methodology and analysis.

Considering the authors' use of the Bower flying wing model, it would be valuable to include a comparison of results from VLM with their own findings to enrich the discussion and provide further insights.

5. Term "center airfoil": The term "center airfoil" is not commonly recognized in the field of aerodynamics or aircraft design. It would be more appropriate to use a more widely accepted term, such as "airfoil at the centerline" or another precise descriptor to avoid ambiguity.

 

some minor spelling error wound

226   wise distribution of the forces from from medium-fidelity vortex lattice methods and

532  since been described. Due to the twist distribution used to produce this spandload

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Authors have addressed the points raised by the reviewer to a sufficient extent which is appreciated.

Author Response

Reviewer 2: 

Thanks for your helpful comments on revision 1 and time taken to verify the suggested changes. 

Reviewer 3 Report

The authors include some of the comments. I find this OK, but after they included the Fig. 4 and after careful observation I can notice that the wings from Fig 3. and Fig 4. are two different wings with different taper ratio and leading edge sweepback angle. The authors should explain this and fix this if possible.

Also, the part of this research (CFD results for twisted wing) was previously published in 2 different papers that authors did not cite within paper and I strongly suggest to do that. Also, better geometry description is given within those papers.

1. Scott M. Weekley, Ryan C. Paul and Jamey D. Jacob. "Design and Testing of Bellwether: A Flying Wing Featuring the Bell Span-Load," AIAA 2021-2438. AIAA AVIATION 2021 FORUM. August 2021.

2. Caleb S. Robb, Rohit K S S Vuppala, Ryan C. Paul and Kursat Kara. "Flight Dynamics of a Flying Wing Aircraft Featuring the Bell Spanload," AIAA 2023-2610. AIAA SCITECH 2023 Forum. January 2023.

Author Response

Reviewer 3:

Thank you for your additional comments. Figure 3 and Figure 4 were added per reviewer comments during the first revision. Please note that Figure 4 is a slightly oblique view compared to Figure 3, which looks straight down on the wing. This rotation makes the CFD discretization in Figure 4 more apparent. We checked our CAD model that forms the basis for the CFD, and measured the sweep, root and tip chord, and resulting taper ratio. We affirm that these values are equivalent to the VLM model. Note that the CFD model has a slightly rounded tip feature that allows a physically realized version of the aircraft to be released after a composite molding process.

We have cited the suggested previous work in a manner we consider appropriate. Suggested citation #1 focused on a different configuration, but the relevant component of the work has been highlighted. Suggested citation #2 was considering roll-yaw coupling effects for the configuration under analysis in this manuscript.

Round 3

Reviewer 3 Report

No further suggestions.