Generalization Capability of Convolutional Neural Networks for Progress Variable Variance and Reaction Rate Subgrid-Scale Modeling
Round 1
Reviewer 1 Report
This paper deals with the generalization capability of the SGS modeling driven by the convolutional neural network. It hasn't been handled, still, in the society of combustion, so it will engage the reader's attention. In my opinion, this paper has quality, because the author tried to encompass the predictive power of the neural network for the different inlet velocity fluctuations and the filter widths. However, some minor revisions are necessary before publication.
- In section 6, the PB-CNN model is analyzed but it doesn't provide quantitative error metrics. Moreover, a hexbin plot for the R2 generalization set is omitted for the R2 generalization case. This paper is looking into the generalization capability of the neural network and it touched heavily on Pfitzner beta PDF closure in the theory part, thus it is recommended to be supplemented.
- It is connected to the previous point, the Pfitzner source term model which is the version used in this study is under the assumption of single-step chemistry. The R2 DNS, however, used sets of chemistry steps. It will create error unexpected. The author can refer to this paper, "An analytic probability density function for partially premixed flames with detailed chemistry", Physics of Fluids, 33, 035117 (2021) (doi: 10.1063/5.0038888). I would like to hear the author's opinion.
- In my opinion, retaining the three key ratios, if we want to apply the trained network to the other test cases, is a big limitation for practical use. The author adjusted these ratios but it deteriorates the performance. The author mentioned at the line of 388 that there must be a certain filter size matching the model across a range of filter sizes. However, in my opinion, it can be predicted that it will make the overall error levels increase. I would like to hear the author's opinion.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper is well written and it is on a timely topic. So, this reviewer recommends to accept this paper for publication, subject to amending appropriate corrections to the manuscript to address the following comment.
The algebraic closure for SGS variance in Eq. 17, introduced originally in Ref. [21] is for a conserved scalar like mixture fraction but progress variable is not a conserved scalar and thus the use of this closure must be justified clearly. Ref. [15] noted that this algebraic closure may yield "correct" behavior for "wrong" reasons on the physical grounds. This is discussed clearly in Ref. [15] and the authors seem to have ignored this although they have cited [15] - hard to understand why? This must be discussed clearly in section 2.3.
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
The paper suggests a convolutional neural network based approach for obtaining the reaction progress variable variance for the sub-grid scale modelling of the reaction rate, in premixed, adiabatic combustion. The approach is quite in line with the recent endeavours in utilizing deep learning and neural network methods in modelling turbulent combustion, and represents a very interesting contribution. The research work is presented in a quite structured and clearly and the paper is well written. Still there are points that need further clarification. The paper shall be revised in the points listed below:
1. Line 184: What is exactly meant by “A velocity profile corresponding to laminar flame propagation” ?
2. Line 193: It would be better to write “mesh size to the Kolmogorov scale” since the corresponding equation follows this order.
3. In Section 3.1, it seems that there are questions in the described HIT case. The chosen values for u’/SL and lt/delta_l (as well as the corresponding Damköhler and Karlovitz numbers) correspond to the Well Stirred Regime in the well-known Borghi’s diagram. However, the reaction progress variable formulation of combustion (Eq. (1)) which goes back to the work of Bray et al, assumes a comparably fast chemistry, i.e. high Damköhler number, i.e. rather of laminar flamelet regime of combustion.
Thus, the basis of the mathematical model and the prescribed parameters of the test case seem to be in contradiction. This point needs to be clarified.
4. Section 3.2 (R2 slot burner jet flame): The flame shall also be described in terms of u’/SL and lt/delta_l /similar (to the previous flame) and its combustion mode with respect to the Borghi diagram shall be identified. Thus, the difference shall also be demonstrated in this perspective.
5. Section 4.2: The condition that “Delta/delta_L” is kept constant at 0.81 is difficult to understand, since delta_L, being the “laminar” flame thickness, should not change as Delta changes. And why exactly this number “0.81” ?
Author Response
Please the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
The authors have sufficiently answered my questions. The revised paper can be accepted for publication.
