Nonintrusive Aerodynamic Shape Optimisation with a POD-DEIM Based Trust Region Method

Round 1

Reviewer 1 Report

The manuscript describes a new surrogate-based optimisation strategy using a POD-DEIM ROM to replace full order CFD simulations. The ROM uses the POD-DEIM to reconstruct surface flowfields of the quantities of interest. The topic is interesting and novel, however, the innovation needs to be documented and highlighted so that the added value to the literature is sound and clear. According to the reviewer, the manuscript requires some minor revisions before it can be considered for possible publication, as some aspects of the manuscript need to be clarified.

 

General Comments

1)      The reviewer believes that the introduction section can be improved by clearly highlighting the innovation of the presented study. The added value to the literature must be documented.

Comments on the manuscript

1)      P1 L3 Computational Fluid Dynamics is mentioned, the abbreviation must be also written there (CFD), because in the rest of the document the abbreviation “CFD” is documented.

2)      P2 Abbreviation Section: CL and CD have the wrong explanation, please improve

3)      P4 L76: There is a repetition of the words “of the”

4)      Eq(1): Please provide a reference for equation 1.

5)      P4 L81: The reviewer believes that more details regarding the design parameters μ must be given for completeness. Please improve.

6)      P4 L80: The meaning of ρU and ρΕ must be explained, in the abbreviation section

7)      P5 L96: The authors mention “set of basis”, the reviewer believes that a brief explanation about this set must be given.

8)      P5 L113 Please provide a reference about Matlab

9)      P6 L124 A trust region is set up with n1=0.8 and n2=1.20, it is suggested to explain the reason for setting these figures for the study.

10)   P6 L129 & L130 Please provide references for the test cases.

11)   Fig2a and 2b do not exist only Figure 2

12)   P8 L153 Please briefly explain why you set for target values these specific figures (M, Re, n, α)

Author Response

The authors would like to thank the reviwer for his/hers constructive comments. The reviewers comments are listed below, with each entry followed by our reply. The new manuscript highlights these changes in red.

R: The reviewer believes that the introduction section can be improved by clearly highlighting the innovation of the presented study. The added value to the literature must be documented.

A: the penultimate paragraph of the introduction was modified to emphasise the key methods developed in this work.

Comments on the manuscript

• P1 L3 Computational Fluid Dynamics is mentioned, the abbreviation must be also written there (CFD), because in the rest of the document the abbreviation “CFD” is documented.
  • Fixed as requested
• P2 Abbreviation Section: CL and CD have the wrong explanation, please improve
  • corrected as requested
• P4 L76: There is a repetition of the words “of the”
  • item removed from text
• Eq(1): Please provide a reference for equation 1.
  • new reference included (ref.34)
• P4 L81: The reviewer believes that more details regarding the design parameters μ must be given for completeness. Please improve.
  • detailed added specifying μ as the optimiser's design variables. (P4, l106-107)
• P4 L80: The meaning of ρU and ρΕ must be explained, in the abbreviation section
  • definitions added to nomenclature
• P5 L96: The authors mention “set of basis”, the reviewer believes that a brief explanation about this set must be given.
  • the term T_M was added to the sentence to clarify which basis we referred to and complete the solution to eq. 3.
• P5 L113 Please provide a reference about Matlab
  • reference added(ref.35).
• P6 L124 A trust region is set up with n1=0.8 and n2=1.20, it is suggested to explain the reason for setting these figures for the study.
  • these values can be tuned for each case, our experiments show that the values cited perform adequately over a wide range of problems; this explanation was added to the text (P6,l148/9).
• P6 L129 & L130 Please provide references for the test cases.
  • references added (ref. 36 & 37)
• Fig2a and 2b do not exist only Figure 2
  • Figure added and there is now a figure 3-a) & 3-b)
• P8 L153 Please briefly explain why you set for target values these specific figures (M, Re, n, α)
  • This is a common test case used in the validation of CFD solvers and subsequently, optimisers. Hence, this was selected to facilitate bech-marking . This justification and relevant reference was added to P7, l152.

 

 

Reviewer 2 Report

The manuscript entitled "Non-intrusive aerodynamic shape optimisation with a POD-DEIM based Trust-Region Method" has been investigated in detail. The topic addressed in the manuscript is potentially interesting and the manuscript contains some practical meanings, however, there are some issues which should be addressed by the authors:

 

1.      Highlights are not written. Please add this part.

2.      The Introduction section needs a major revision in terms of providing more accurate and informative literature review and the pros and cons of the available approaches and how the proposed method is different comparatively. Also, the motivation and contribution should be stated more clearly.

3.      The analysis on the results is weak. Analyze the results more fully.

4.      Add more explanation about uncertainty analysis?

5.      Make it clear which hypothesis you want to validate.

6.       

7.      Add the details about the grids. Meanwhile, conduct the grid convergence testing.

8.      In Figs. 3-4 and 6 what is the used Reynolds number?

9.      The governing equations should be expressed in full, The flow is compressible, so the energy equation must be solved.

10.  The paper needs to be checked carefully for grammatical mistakes.

11.  What algorithm and method has been used to optimize the geometric shape?

 

Author Response

The authors would like to thank the reviwer for his/hers constructive comments. The reviewers comments are enumerated below, with each entry followed by our reply. The new manuscript highlights these changes in blue.

1. Highlights are not written. Please add this part.
   • Highlights have been added, page 1.
2. The Introduction section needs a major revision in terms of providing more accurate and informative literature review and the pros and cons of the available approaches and how the proposed method is different comparatively. Also, the motivation and contribution should be stated more clearly.
   • the introduction has been revised, it includes over 30 references appraising adjoint, surrogate and model reduction techniques in the context of aerodynamic shape optimisation. The proposed method conntributions are clarified and described in page 3, lines 87-97.
3. The analysis on the results is weak. Analyze the results more fully.
   • results have been expanded including grid convergence results for both cases (fig. 2 & table 1), further analysis of case 1 constrained optimisation (page 10, lines 220-223 & fig. 11), further analysis of case 2 (page 11, lines 236-241; page 13, lines 260-267, figures 14 &16), including span load analysis.
4. Add more explanation about uncertainty analysis?
   • The paper does not perform uncertainty analysis; if necessary, could the reviewer please clarify what he/she has in mind?
5. Make it clear which hypothesis you want to validate.
   • The paper's aims have been clearified in the introduction, page 3, lines 87-97.
6. Add the details about the grids. Meanwhile, conduct the grid convergence testing.
   • Grid convergence studies were added, fig. 2 & table 1, together with supporting descriptions.
7. In Figs. 3-4 and 6 what is the used Reynolds number?
   • fig.3-4 (now fig 4-5) test conditions have been added/clarified (page 7, line 176/5); fig. 6 (now 7) refers to the test case defined in the paragraph preceeding eq.9.
8. The governing equations should be expressed in full, The flow is compressible, so the energy equation must be solved.
   • the energy eq. is solved. The solver used is described in ref. 38, the text now emphasizes that the the compressible form of the RANS equations are solved. We prefer not detailing the flow equations to avoid overloading the mathematical formulation with methods that are already well documented in the literature, instead we direct the readers to the paper documenting SU2, i.e. ref.38, which includes the full details of the equations solved, including the turbulence model and respective implementation.
9. The paper needs to be checked carefully for grammatical mistakes.
   • the paper has been further reviewed and corrected.
10. What algorithm and method has been used to optimize the geometric shape?
    • The optimisation subproblem is solved using MatLab’s fmincon, this is detailed in page 5, line 141-142; the shape is deformed by an RBF morphing method, as detailed in page 7, line 170/1.

Reviewer 3 Report

The introduction section is too long. From 1.1 to 1.5 subsections are about methods used in the paper, I suggest add a section describe these methods.

Author Response

The authors would like to thank the reviwer for his/hers constructive comments. The reviewers comments are listed below, with each entry followed by our reply. The new manuscript highlights these changes in dark green.

Reviewer: The introduction section is too long. From 1.1 to 1.5 subsections are   about methods used in the paper, I suggest add a section describe these methods.

• the authors agree with the comment, sections 1.1 to 1.5 are now 2.1-2.5

 

Round 2

Reviewer 2 Report

All my comments have been thoroughly addressed. It is acceptable in the present form.