FEA-Based Thermo-Structural Modeling of Cryogenic Storage Tanks in Liquid Propulsion Systems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This brief paper presents an FEA analysis of cryogenic tanks operating at two different pressure conditions and three different temperature conditions. The authors use a commercial code (StarCCM+) to calculate von Mises stresses and resulting safety factors in all six conditions of the parameter space, while they also conduct a mesh independence study for one of the 6. The paper, at 14 pages including many figures, tables, and references is a very brief piece of work that practically finishes at the level of validation. The paper should be published when the authors augment their discussion with more results and deeper - and more critical - discussion of their findings. Specific comments follow.

 

The authors should provide actual sizes of the vessels they are modeling, as well as some of the more significant aspects of the tanks. This becomes important when they state that their mesh varies from 1 m, to 0.1m, to 0.01 m. These do not make a lot of sense, unless they are explained as fractions of the tank features. Equally important for the validity of the FEA is the characterization of the curvature and size of the tubular structures at the top and bottom of the tanks, since these are the locations of maximum stress concentration.

 

In their paper the V&V comes last, after the results have been presented, somewhat akin to "putting the cart before the horse". Validation and/or verification of the frameworks and the models is supposed to precede the results, so as to project confidence for what is to follow.

 

The insistence on using the safety factor (FoS) as a metric of mesh convergence  is clearly not working here. For some reason the coarser mesh produces smaller maximum stress and therefore higher FoS. This belies the rest of the results, where the FoS of approximately 2 is declared sufficient for tank design. Is there any confidence that a finer mesh would not produce an FoS of 1.5, or something similar? The authros must provide a clear explanation as to why this change happens in their FEA, and prove that there is a level of convergence with the mesh they are using. At the moment it does not look like there is any, rather FoS numbers that keep changing with different mesh size. The paper states that "[I]n each case, the FoS values varied, but after a certain level of refinement, the changes became negligible, indicating that the mesh had reached a sufficient level of resolution to accurately represent the cryogenic tank behavior", but Table 5 belies that point by showing significant variations. .Additionally, as discussed already, what is the meaning of 1-m mesh resolution?

The modeling needs to be explained a bit better. The discussion of thermal stress and yield need to be quantified with clear graphs and/or tables. The full air/solid/liquid setup is a conjugate heat transfer type of problem and unless the authors treated it as such, some level of simplification took place. They must explain that clearly in their initial modeling section, and explain in the results how they calculate or model heat flux from air to solid, to liquid. 

 

One general comment regarding the references used in the paper: some are internal reports that are inaccessible to the general reader, and many are from sources that are not usually associated with journal publications, like manuals, teaching resources and textbooks. The authors should attempt to connect their results with past research in the topic of FEA and thermal stress analysis in cryogenic tanks.

 

 

Author Response

Comments and Suggestions for Authors

General Comments: This brief paper presents an FEA analysis of cryogenic tanks operating at two different pressure conditions and three different temperature conditions. The authors use a commercial code (StarCCM+) to calculate von Mises stresses and resulting safety factors in all six conditions of the parameter space, while they also conduct a mesh independence study for one of the 6. The paper, at 14 pages including many figures, tables, and references is a very brief piece of work that practically finishes at the level of validation. The paper should be published when the authors augment their discussion with more results and deeper - and more critical - discussion of their findings. Specific comments follow.

Answer:

The authors thank the reviewer for the thoughtful summary and constructive feedback. In response, the Discussions section has been expanded to include a more in-depth analysis of the results. The authors hope these additions provide a more complete and reflective discussion of the findings in this work.

 

 

 Question 1: The authors should provide actual sizes of the vessels they are modeling, as well as some of the more significant aspects of the tanks. This becomes important when they state that their mesh varies from 1 m, to 0.1m, to 0.01 m. These do not make a lot of sense, unless they are explained as fractions of the tank features. Equally important for the validity of the FEA is the characterization of the curvature and size of the tubular structures at the top and bottom of the tanks, since these are the locations of maximum stress concentration.

Answer:

The authors thank the reviewer for this valuable observation. To provide better context for the mesh sizes used in the simulation, we have now included Figure 3, which illustrates the full set of geometric dimensions of the cryogenic tank, including the curved nozzles at both ends where stress concentrations were observed.

Additionally, the mesh sizes referenced in the manuscript (1.0 m, 0.1 m , 0.01 m) refer to base size inputs in Star-CCM+, serving as starting points for automatic mesh generation — not fixed element dimensions. Star-CCM+ adapts the mesh locally, refining it automatically in complex areas like curves and junctions, even when the global base size is large. The authors hope this clarification and the added figure fully address the reviewer’s concerns and improve the technical clarity of the manuscript.

 

 Question 2: In their paper the V&V comes last, after the results have been presented, somewhat akin to "putting the cart before the horse". Validation and/or verification of the frameworks and the models is supposed to precede the results, so as to project confidence for what is to follow.

 Answer:

The authors thank the reviewer for this thoughtful and important comment. In response, the Mesh Independence Study has been moved earlier in the manuscript and is now presented as Section 4.0, preceding the Results section (now Section 5.0). This reorganization ensures that the verification of the simulation framework is addressed before discussing the results, providing more confidence in the model’s fidelity and accuracy.

 

 

 

 

 

 

Question 3: The insistence on using the safety factor (FoS) as a metric of mesh convergence  is clearly not working here. For some reason the coarser mesh produces smaller maximum stress and therefore higher FoS. This belies the rest of the results, where the FoS of approximately 2 is declared sufficient for tank design. Is there any confidence that a finer mesh would not produce an FoS of 1.5, or something similar? The authros must provide a clear explanation as to why this change happens in their FEA, and prove that there is a level of convergence with the mesh they are using. At the moment it does not look like there is any, rather FoS numbers that keep changing with different mesh size. The paper states that "[I]n each case, the FoS values varied, but after a certain level of refinement, the changes became negligible, indicating that the mesh had reached a sufficient level of resolution to accurately represent the cryogenic tank behavior", but Table 5 belies that point by showing significant variations. .Additionally, as discussed already, what is the meaning of 1-m mesh resolution?

Answer:

The authors sincerely thank the reviewer for highlighting this important point regarding mesh convergence and the use of factor of safety (FoS) as a metric to evaluate the Mesh Independence Study. To clarify, the authors were using FoS values to help communicate the relevance of the observed Von Mises stress changes as the mesh was refined. However, the primary metric for evaluating mesh convergence was the maximum Von Mises stress, not FoS directly.

The authors acknowledge that the previous Mesh Independence Study did not show an acceptable convergence behavior. To correct this, the authors extended the Mesh Independence Study, analyzing five total cases of mesh base size values (1 m, 0.1 m, 0.01m, 0.009 m, and 0.008 m). By extending the mesh study beyond a base size of 0.01 m, the variation in maximum Von Mises stress becomes less than 1.2% between base sizes of 0.01 m, 0.009 m, and 0.008 m. This negligible change in maximum Von Mises stress results demonstrates mesh convergence and justifies the choice of a base size of 0.01 m as an optimal mesh resolution. Additionally, to visually confirm mesh convergence, a plot of maximum Von Mises stress vs. number of elements (Figure 11) was added.

Lastly, as clarified in the response to Question 1, the 1 m mesh size resolution refers to the base size input in Star-CCM+, which dictates the initial cell sizing before adaptive local refinement. It does not imply that elements are uniformly 1 meter in size. Furthermore, the definition of the mesh base size has been included in the Methodology section of the manuscript to reflect this clarification more explicitly.

 

 

 

 Question 4: The modeling needs to be explained a bit better. The discussion of thermal stress and yield need to be quantified with clear graphs and/or tables. The full air/solid/liquid setup is a conjugate heat transfer type of problem and unless the authors treated it as such, some level of simplification took place. They must explain that clearly in their initial modeling section, and explain in the results how they calculate or model heat flux from air to solid, to liquid. 

Answer:

The authors thank the reviewer for this helpful comment. The manuscript now clarifies in the Methodology section that a simplified approach was used in place of a full conjugate heat transfer model. Constant temperatures were applied at the inner and outer walls of the tank geometry to represent the saturation temperatures of each cryogenic fluid and ambient temperature, respectively. Due to this simplified approach, no heat flux calculations were performed in the analysis.

To address the request for clearer stress quantification, Table 5 summarizes the maximum Von Mises stress, material strength, and factor of safety (FoS) for all cases. The authors hope this explanation resolves the reviewer’s concern.

 

Question 5: One general comment regarding the references used in the paper: some are internal reports that are inaccessible to the general reader, and many are from sources that are not usually associated with journal publications, like manuals, teaching resources and textbooks. The authors should attempt to connect their results with past research in the topic of FEA and thermal stress analysis in cryogenic tanks.

Answer:

The authors thank the reviewer for this important suggestion. Several references have now been added to the Discussions section to include peer-reviewed publications and journal articles related to FEA and thermal stress analysis in cryogenic tanks. This helps the manuscript to provide a better connection between the present work and past investigations.

 

 

 

 

 

 

Reviewer 2 Report

Comments and Suggestions for Authors

• Please show the temperature distribution, as it significantly affects thermal stresses.
• The ends of both flanges are fixed in the analyses. Is this boundary condition correct? If the longitudinal dimension is constrained, the cooled tank shrinks, generating a tensile force that causes stress at the base of the flange. In general, a flexible pipe is used to avoid such tensile force.
• What does it mean that the mesh size is 1m? Although the thickness of the tank is not stated, it should be much thinner than 1m. The mesh size should be even thinner than the tank thickness.
• As stated at the end of Chapter 4, the mesh size must be fine enough that the effect can be neglected. Even with a mesh size of 0.01, changes in the FoS can still be seen, so it cannot be said to be fine enough.

Author Response

Comments and Suggestions for Authors:

 

Question 1: Please show the temperature distribution, as it significantly affects thermal stresses.

Answer:

The authors thank the reviewer for this helpful comment. To better illustrate the influence of temperature on thermal stress, Figures 14, 15, 18, 19, 22, and 23 have been added to the Results section, showing the temperature contours for all the examined cases.

 

 

Question 2: The ends of both flanges are fixed in the analyses. Is this boundary condition correct? If the longitudinal dimension is constrained, the cooled tank shrinks, generating a tensile force that causes stress at the base of the flange. In general, a flexible pipe is used to avoid such tensile force.

Answer:

The authors thank the reviewer for this insightful observation. The fixed-end boundary condition was applied as a simplified assumption to evaluate the structural response under constrained conditions. A clarifying statement has now been stated in the Methodology section to explain the reasoning behind the application of these boundary conditions.

 

 

 

 

 

Question 3: What does it mean that the mesh size is 1m? Although the thickness of the tank is not stated, it should be much thinner than 1m. The mesh size should be even thinner than the tank thickness.

Answer:

The authors appreciate the reviewer’s comment and the opportunity to clarify this concern. The 1 m mesh size refers to the base size input in Star-CCM+, which is used as a global reference for mesh generation — not the actual element size. Star-CCM+ automatically refines the mesh in thin and curved regions, such as the 7 mm-thick tank wall, to ensure proper resolution. Furthermore, this clarification has been added to the Methodology section, along with the tank’s full geometry details in Figure 3.  

 

 

Question 4: As stated at the end of Chapter 4, the mesh size must be fine enough that the effect can be neglected. Even with a mesh size of 0.01, changes in the FoS can still be seen, so it cannot be said to be fine enough.

Answer:

The authors thank the reviewer for this important observation. To address this issue, the Mesh Independence Study was extended to include two additional mesh refinements beyond the 0.01 m base size, resulting in a total of five cases: 1 m, 0.1 m. 0.01 m, 0.009 m, and 0.008 m. The maximum Von Mises stress, which is used as the primary convergence metric, showed changes of less than 1.2% between the three finest meshes (0.01 m, 0.009 m, and 0.008 m), indicating sufficient mesh convergence. This update is now clearly reflected in Section 4 of the manuscript, along with the corresponding convergence plot shown in Figure 11.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors addressed the main concern of the first review regarding using the safety factor as a metric of grid independence and convergence, by concentrating on the von Mises stress instead. They make a case that increasing the grid resolution increases that stress, and argue that a converged mesh will produce the maximum stress (and minimum safety factor). But one more major issue must be addressed regarding the convergence. The results shown in figure 11 and table 4 do not conclusively prove that mesh independence, because the number of elements does not vary substantially in the last three cases with the highest element count. There is little variation in von Mises stress, but that could very well be due to the proportionally small variation in the number of elements. If the mesh was refined by, say, a factor of 50%, there is no guarantee that the stress would remain converged at the level they have identified right now. Along the same lines, the manner of plotting in figure 11 ends up being misleading, since the three highest-count cases are denoted by points that are spread apart far, far more than they should along the horizontal axis. As a result, the all-important safety factor may end up being quite a bit smaller than 2, and the whole point of the paper may become moot.

 

The authors attempted to answer another major point of the first review, namely the lack of scientific results and discussion, but chose to address that by simply adding a couple of pages of figures with temperature gradient results from different cases. At the end the whole paper ends up looking like is a mesh independence study that is not conclusive, or even well posed. The commercial code (Star CCM+) is used as a 'black box', so much so that there is no well-defined variable for the parametric study, except the "mesh base size" input to the code. This is a parameter used internally by the code, without explicit control of the user, and conducts refinement of the grid automatically, where it is deemed necessary. That is not a valid approach for a scientific study to be published in a journal article.

Author Response

Question 1: The authors addressed the main concern of the first review regarding using the safety factor as a metric of grid independence and convergence, by concentrating on the von Mises stress instead. They make a case that increasing the grid resolution increases that stress and argue that a converged mesh will produce the maximum stress (and minimum safety factor). But one more major issue must be addressed regarding the convergence. The results shown in figure 11 and table 4 do not conclusively prove that mesh independence, because the number of elements does not vary substantially in the last three cases with the highest element count. There is little variation in von Mises stress, but that could very well be due to the proportionally small variation in the number of elements. If the mesh was refined by, say, a factor of 50%, there is no guarantee that the stress would remain converged at the level they have identified right now. Along the same lines, the manner of plotting in figure 11 ends up being misleading, since the three highest-count cases are denoted by points that are spread apart far, far more than they should along the horizontal axis. As a result, the all-important safety factor may end up being quite a bit smaller than 2, and the whole point of the paper may become moot.

Answer:

We sincerely thank the reviewer for this thoughtful and constructive comment. We greatly appreciate the opportunity to clarify the mesh independence study and fully recognize the importance of demonstrating numerical consistency with precision and transparency. The reviewer’s insights prompted us to revise and strengthen the technical depth of this section, which has now been substantially improved in the manuscript.

We would also like to acknowledge and correct an oversight in our original submission: the mesh sizes reported in the earlier version mistakenly included the cell count instead of the actual number of elements in the mesh. This occurred due to a misinterpretation of Star-CCM+’s default mesh reporting. After identifying the issue, we utilized Star-CCM+’s diagnostic tools to extract the correct number of elements for each case. These corrected values are now reflected in both Table 4 and Figure 12 of the revised manuscript. We sincerely appreciate the reviewer’s comment, which led us to recognize and correct this important detail.

To address the concern about the conclusiveness of our mesh independence study, Section 4.0 has been revised to explicitly document the refinement behavior and element count variation across all six mesh cases. We focused on both the factor of safety and von mises stress behavior for mesh convergence study, as this combination showed more stable trends and better reflection on structural reliability. For instance, when doing mesh independence study, from Case 4 to Case 5, the number of elements increased by approximately 30%, with only a 6% change in the von Mises stress. A further 4% increase in elements from Case 5 to Case 6 resulted in just a 1% decrease in stress, with no change in the computed factor of safety, which remained at 2.0. This pattern reflects a clear stabilization in stress values, indicating convergence. The authors would like to emphasize that each of the mesh cases between 4 and 6 required substantial computational effort, with long initialization and simulation times. The simulations were conducted using the maximum available cores and the finest mesh resolution feasible on our current workstation. Based on the observed trend in the results, we are confident that further refinement would yield only marginal changes and is unlikely to significantly impact the outcome. Therefore, considering both the extended analysis and practical computational constraints, the selected mesh represents a reasonable and reliable choice that balances numerical accuracy with computational efficiency.

Regarding the reviewer’s point about the plotting method, we agree that the previous version of Figure 11 (now Figure 12) may have presented an unintentionally misleading visual impression due to uneven spacing along the x-axis. This figure has been redesigned to use uniform horizontal intervals, offering a more clear depiction of the refinement steps and convergence trend.

We have also clarified that the mesh base size was the only parameter varied during the mesh refinement process. All other mesh settings, including meshing method, quality threshold, volume growth rate, and number of thin layers, were held constant. Furthermore, we expanded the explanation of how mesh base size functions in Star-CCM+ as a global control parameter that proportionally defines surface and volume element sizing throughout the geometry, ensuring uniform refinement even in regions with complex features.

Lastly, with respect to the reviewer’s concern about the safety factor potentially dropping below 2.0, we would like to clarify that our study does not treat 2.0 as an absolute safety threshold. The structural integrity criterion was based on a minimum factor of safety of 1.0, and all mesh cases in our study, including the most refined ones, maintain a safety factor comfortably above this limit. The last three mesh cases converge at or near a safety factor of 2.0, and given the stress stabilization observed, we are confident that further refinement would not significantly alter this outcome.

We are grateful for the reviewer’s detailed feedback, which has helped us improve the technical clarity, accuracy, and transparency of this section. We believe the revised manuscript now presents a more robust and well-supported mesh independence study.

Question 2: The authors attempted to answer another major point of the first review, namely the lack of scientific results and discussion, but chose to address that by simply adding a couple of pages of figures with temperature gradient results from different cases. At the end the whole paper ends up looking like is a mesh independence study that is not conclusive, or even well posed. The commercial code (Star CCM+) is used as a 'black box', so much so that there is no well-defined variable for the parametric study, except the "mesh base size" input to the code. This is a parameter used internally by the code, without explicit control of the user, and conducts refinement of the grid automatically, where it is deemed necessary. That is not a valid approach for a scientific study to be published in a journal article.

Answer:

We sincerely thank the reviewer for this valuable comment and for highlighting areas that required clarification. We deeply appreciate the opportunity to improve the quality of the manuscript and to better explain the purpose, methodology, and insight of the study.

We understand the concern that the mesh independence study appeared to dominate the manuscript in its earlier form. This was certainly not our intention, and we appreciate the opportunity to clarify and better balance the presentation of the study. The mesh independence section was emphasized in the previous revision with the intention of ensuring transparency in the accuracy and reliability of the numerical results. However, we recognize that the original presentation may have lacked sufficient integration with the broader scientific analysis, and we thank the reviewer for pointing this out.

In response, we have substantially revised Sections 5.0 through 5.4 to expand the scientific discussion and more clearly present the engineering insights derived from the simulations. These sections now provide detailed comparisons of temperature gradients, Von Mises stress distributions, and factors of safety across six loading cases, encompassing different cryogenic fluids and internal pressures. The analysis interprets the structural response in the context of thermal contraction effects and clearly identifies regions of stress concentration—particularly at the nozzle-shell interface—while showing that the main tank body experiences relatively uniform low stress. We also discuss the dominant influence of thermal gradients by comparing full thermo-structural results against pressure-only cases. To further contextualize the findings, we have incorporated relevant references from the literature, providing a stronger scientific foundation for our observations.

We respectfully clarify that in the mesh independence study presented in Section 4.0, the mesh base size was the only parameter varied in order to evaluate the effect of global mesh refinement on stress results. In Star-CCM+, the mesh base size is a user-defined input that provides consistent control over the target size of both surface and volume elements throughout the domain. Although we understand the reviewer’s concern, we note that this parameter is not controlled internally by the software. Instead, it is explicitly set by the user and directly influences the resolution of the mesh, allowing for structured refinement and progressive improvement in mesh quality as element density increases. The mesh base size was selected because it enables a uniform and scalable method for refining element resolution across the domain. All other parameters, including the meshing method, number of thin layers, growth rate, and quality threshold, were kept fixed to ensure that the only varying factor was overall element density. The team believes that convergence was reasonably achieved in the final cases, as the Von Mises stress results showed consistent stabilization, supporting the validity of the refinement approach and the reliability of the stress results for the objective of this study.        

We sincerely thank the reviewer once again for this valuable feedback, which allowed us to greatly improve the clarity, transparency, and overall scientific rigor of the manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

All the points that I pointed out were corrected.

Author Response

Comments and Suggestions for Authors: All the points that I pointed out were corrected.

 

Authors Response: We sincerely thank the reviewer for the valuable feedback and suggestions throughout the review process. We appreciate the acknowledgment of our efforts and the acceptance of our responses. We truly believe that our paper will contribute meaningfully to thermo-structural research on cryogenic systems, particularly for LOX-LCH₄ propulsion systems in space exploration. Therefore, we respectfully urge the reviewer to recommend our paper for publication.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

The authors addressed most of the issues raised during review, and in particular the issue of V&V in their calculations. The scientific discussion of some of their results is also a welcome addition to the paper