Calibration of Turbulent Model Constants Based on Experimental Data Assimilation: Numerical Prediction of Subsonic Jet Flow Characteristics
Round 1
Reviewer 1 Report
This study utilizes the ensemble Kalman filter algorithm to recalibrate turbulence model constants by integrating experimental data and numerical simulations. The modified model improves jet flow prediction accuracy, reducing relative errors and providing insights for aircraft safety and airport operational efficiency. However, before further consideration of the manuscript, the authors must “fully” address the comments listed below:
1- In the context of this study, how does the ensemble Kalman filter algorithm play a pivotal role in recalibrating the SA turbulence model constants to accurately predict the flow characteristics of subsonic jet exhaust? Can you provide a detailed explanation of how the algorithm integrates NASA's experimental particle image velocimetry (PIV) data with a sample library generated using Latin hypercube sampling to obtain corresponding flow field calculations?
2- What specific improvements in the prediction of jet flow characteristics are achieved by modifying the turbulence model constants through the ensemble Kalman filter algorithm? Please provide a detailed analysis of the reduction in spatially averaged relative error along the horizontal axis behind the nozzle, comparing the values before and after the recalibration process. Additionally, elaborate on the implications of these improvements for accurately predicting subsonic jet flow and discuss the potential impact on safety clearances during aircraft crossing and airport operational efficiency.
3- Could you provide an extensive analysis of the ensemble Kalman filter algorithm, specifically its integration of Kalman filtering with ensemble forecasting? Elaborate on how the algorithm estimates the covariance between state and observation variables by utilizing ensemble forecasts and how the analysis is updated through the incorporation of observation data and covariance. Furthermore, discuss the algorithm's effectiveness in addressing the assimilation problem in nonlinear models, with a focus on turbulent numerical models with high-order nonlinearity. Provide a detailed explanation
4- What are the advantages and limitations of the Spalart-Allmaras (SA) one-equation turbulence model in the context of engineering applications?
5- It is still unclear how the equation 10-11 (Kalman gain calculation and Updating ensemble members) were derived, please provide more explanation.
6- XYZ coordinates are missing from many figures.
7- When considering the error values depicted in Figure 11, do these values conform well to industry standards, and how can these errors be further reduced?
8- Apart from Spalart-Allmaras (SA) model, other strong numerical methods can be employed such as K-Omega Model (https://doi.org/10.1115/GT2022-78306), Bezier Multi-Step Method (https://doi.org/10.1016/j.compstruct.2019.01.041), and Differential Quadrature Method (https://doi.org/10.1016/S0263-8223(97)00112-8). You can briefly introduce these methods (that can efficiently solve the associated differential equations) and reference the referred papers.
9- Conclusion: Can authors highlight future research directions and recommendations? Also, highlight the assumptions and limitations (e.g., shortcomings of the present study). Besides, recheck your manuscript and polish it for grammatical mistakes (you can use “Grammarly” or similar software to quickly edit your document).
Author Response
Dear Reviewer,
We would like to express our gratitude for reviewing our manuscript and providing valuable feedback and suggestions. Your expertise and meticulous review are of utmost importance to our research work, and we deeply appreciate your dedicated efforts.Your constructive comments have positively influenced our study. Your feedback has served as a catalyst for further improvements in our research, and your suggestions will play a crucial role in guiding our future work. We have included our responses to your comments in the attached Word document for your reference.Once again, we sincerely thank you for your diligent work and insightful recommendations. Your professional input has significantly contributed to the advancement of our research.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This study utilizes the ensemble Kalman filter algorithm to recalibrate the SA turbulence model constants by integrating NASA's experimental particle image velocimetry (PIV) data with a sample library generated using Latin hypercube sampling to obtain corresponding flow field calculations. The topic is interesting to the reviewer, there have been significant efforts made to improve the accuracy of the RANS model by many researchers over the years. This manuscript is studying data assimilation in subsonic jet flow, specifically, the SA model is employed for numerical simulations, and ensemble Kalman filtering data assimilation is performed using velocity experimental measurements data from NASA. Eventually, the authors conducted validation and performance comparisons through relevant comparisons of flow field parameters.
The results discussion is clear, the reviewer thinks the idea presented in the paper represents a sizeable effort to improve the accuracy of the SA model and thus the numerical simulations for subsonic jet flows in this case. The manuscript is well written, methods are relatively clearly presented, and some suggestions are listed. The missing piece is the validation. The validation study conducted by the authors is against the original jet flow simulation which is used to generate the data. Since the study goal is to improve the accuracy and broaden the application prospects of turbulent flow research, the question is how well the model will perform in other cases. It’s clear that the current results have proven prediction accuracy improvement in the same application, but similarly many previous works as listed in the literature survey have achieved this. In this case, the authors should make it clear about the contribution and significance of this work, is it to achieve a higher level of accuracy, improve generalizability, or it’s the first time that data assimilation application in a turbulence model? Following that, corresponding validation studies should be conducted and presented.
The following are the suggestions from the reviewer.
1. The most important issue with the current manuscript is the validation work, as mentioned before.
2. The contribution and significance should be clear, if there is a limitation that is reasonable, it should be stated in the manuscript as well.
3. Line 286, the model parameter variation range determined by sensitivity analysis should be set at 50%-150%, how to determine this range?
4. Line 293, why choose 100 sets of samples?
5. Section 3.3, the computational settings need to be expanded a lot. Information such as grid independence study, numerical methods, and order of accuracy should be added to ensure the simulation data are accurate.
6. In Figure 9, is there any explanation for why Relative error drops and then increases for SA+ENKF?
7. Line 401, why the error of the two models also gradually increased at X/D=10, 15, and 20?
8. In the conclusion, some limitations and future work should be added.
Author Response
Dear Reviewer,
We would like to express our gratitude for reviewing our manuscript and providing valuable feedback and suggestions. Your expertise and meticulous review are of utmost importance to our research work, and we deeply appreciate your dedicated efforts.Your constructive comments have positively influenced our study. Your feedback has served as a catalyst for further improvements in our research, and your suggestions will play a crucial role in guiding our future work. We have included our responses to your comments in the attached Word document for your reference.Once again, we sincerely thank you for your diligent work and insightful recommendations. Your professional input has significantly contributed to the advancement of our research.
Author Response File: Author Response.pdf
Reviewer 3 Report
This study employs the ensemble Kalman filter algorithm to recalibrate the SA turbulence model constants by integrating NASA's experimental particle image velocimetry (PIV) data with a sample library generated using Latin hypercube sampling. The idea of the paper is very interesting and it is match the goals of the journal. However, I have some major comments to improve the quality of the paper:
1. Your abstract requires improvement by explicitly addressing the significance of your work, highlighting the innovations presented in your paper, and distinguishing it from comparable studies.
2. Please ensure that the equation fonts are consistent and meet the journal's requirements. It appears that there are inconsistencies in the equation fonts, including instances where equations are displayed in bold.
3. Please ensure that all ticks in the figures are oriented inward. Kindly apply this adjustment specifically to figures 4 and 6.
4. In figure 6, considering that U/Uj is less than 1, it is recommended to commence the y-axis from a value of 1.
5. In equation 17, the left-hand side representing the error was inadvertently omitted. Please include the left-hand side to correctly represent the equation as follows: Error = ...
6. The introduction section requires further elaboration, particularly regarding the methodology employed to solve the equations in the numerical simulation section. Additional explanation is needed to describe how the equations were numerically solved. I appreciate your recommendation to read the suggested papers in order to enhance the clarity and quality of the explanation. https://doi.org/10.1016/j.ijggc.2023.103920 , https://doi.org/10.3997/2214-4609.202183016
7. Please provide a concise overview of the drawbacks associated with your technique and propose potential avenues for improvement in future studies.
8. More explanation needed about Kalman filter algorithm.
9. Overall, the readability of the paper is good and it is easy to follow, but there are some minor English mistakes.
Overall, I think the project is very interesting and after applying these comments it will improve a lot.
Author Response
Dear Reviewer,
We would like to express our gratitude for reviewing our manuscript and providing valuable feedback and suggestions. Your expertise and meticulous review are of utmost importance to our research work, and we deeply appreciate your dedicated efforts.Your constructive comments have positively influenced our study. Your feedback has served as a catalyst for further improvements in our research, and your suggestions will play a crucial role in guiding our future work. We have included our responses to your comments in the attached Word document for your reference.Once again, we sincerely thank you for your diligent work and insightful recommendations. Your professional input has significantly contributed to the advancement of our research.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments are addressed.
Reviewer 2 Report
The authors have addressed all my comments.
Reviewer 3 Report
Thank you to the authors for revising the paper according to my comments and suggestions. I am delighted to announce that this version of the manuscript is now suitable for publication.
