Features of Three-Dimensional Calculation of Gas Coolers of Turbogenerators

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This study improves thermal analysis of hydrogen-water gas coolers in turbogenerators by combining analytical calculations with CFD simulations. The hybrid approach shows less than 10% discrepancy, meets design temperature targets, and reveals nonuniform temperature zones, enabling accurate predictions and design optimisation for enhanced cooling system performance.
It is well-structured, and I provide some minor comments below:
- Emphasise the novelty more clearly in the abstract.
- References [1–3] are overused across unrelated claims; ensure citation accuracy.
- The justification for selecting only the standard k-ε model could be strengthened with comparative data or mesh sensitivity analysis.
- Boundary conditions and mesh convergence should be discussed quantitatively.
- Figures 11–13 are low resolution; colour bars and labels are hard to read.
- Discuss more clearly how the observed thermal nonuniformities can influence machine performance or safety.
- Some references lack proper formatting (e.g., missing journal names or inconsistent DOI formatting).

 

Author Response

We sincerely thank the reviewer for carefully reading our manuscript and providing valuable feedback. Below we address each comment point-by-point and describe the corresponding revisions.

Comment 1: Emphasise the novelty more clearly in the abstract.

Response 1: We agree with your comment and have therefore rewritten the last two sentences of the abstract to more clearly emphasize the novelty of the study.

Comment 2: References [1–3] are overused across unrelated claims; ensure citation accuracy.

Response 2: Thank you for the valuable remark! We agree that references [1–3] were overused, so we reviewed and reduced their number, keeping them only where they are truly relevant.

Comment 3: The justification for selecting only the standard k-ε model could be strengthened with comparative data or mesh sensitivity analysis.

Response 3: We thank the reviewer for this insightful comment. In the Introduction (Lines 90–129), we provided an overview of advanced turbulence models to demonstrate the range of available tools and contextualize the decision-making process. Despite the existence of more advanced alternatives (e.g., Realizable k-ε, SST k-ω), the standard k-ε model was deliberately selected due to its balance between computational cost and accuracy for the specific geometry and flow conditions of the gas cooler under investigation. Our primary goal was to validate a combined analytical–CFD methodology suitable for practical engineering applications where computational resources may be limited. Moreover, the flow regime in the studied case features high Reynolds numbers and lacks strong separation zones, where the standard k-ε model performs reliably. The justification has been added at the end of the Introduction section.

Comment 4: Boundary conditions and mesh convergence should be discussed quantitatively.

Response 4: We agree with your comment. We have added a detailed description of boundary conditions and mesh convergence near Figures 9 and 10 to clarify our numerical modeling process.

Comment 5: Figures 11–13 are low resolution; colour bars and labels are hard to read.

Response 5: Thank you for the helpful remark. We improved the quality and readability of the color scales and labels in Figures 11 and 12. No changes were made to Figure 13, as it is a line plot presented in sufficient resolution for interpretation.

Comment 6: Discuss more clearly how the observed thermal nonuniformities can influence machine performance or safety.

Response 6: Agreed. We have expanded the “Discussion” section to include a brief explanation of how thermal nonuniformities may affect structural stress distributions and should be considered in future mechanical calculations of housing components.

Comment 7: Some references lack proper formatting (e.g., missing journal names or inconsistent DOI formatting).

Response 7: Disagree. In the reference list, only item [3] lacks a DOI and journal name because it refers to a textbook, not a journal article. All other references follow the formatting style and contain full citation information.

Reviewer 2 Report

Comments and Suggestions for Authors

I have listed a few comments to improve the clarity of the manuscript:

1. Citation is missing for the paragraph in Line 130.
2. In Line 345 (Methodology section), we read: "The standard k-ε model is the most widely used...".
   On the other hand, from Line 90 to Line 129, the authors explain several improved versions of the base model (k-ε), as well as some hybrid CFD approaches with improved accuracy and additional features.
   In other words, if the authors used the standard k-ε model, the Introduction should briefly justify its selection in light of existing alternatives.
   Alternatively, if the Introduction presents models better than k-ε, the question arises: why was the base model employed?
3. In Line 110, the phrase “model SST k-ω мод” includes a non-English word ("мод") — this should be corrected.
4. In Line 207, the words “Назва параметру Значення” are non-English and should be translated into English (e.g., “Parameter name / Value”).
5. In Table 2, “hight” should be corrected to “height”.
6. In Line 359, again, “hight” should be corrected to “height”.
7. There are incomplete sentences in Lines 248, 251, and 252 — they need revision for grammatical completeness.
8. In Figure 5, the x-axis and y-axis labels are unclear. What do "Δt/Δt**" and "**Δt``/Δt" represent? Please clarify.
9. The colour maps in Figures 11 and 12 are not legible — use more distinguishable colour gradients or annotate the range for clarity.
10. The Discussion section is too brief and does not adequately contextualise or reflect on the findings. It should be expanded.
11. The Conclusion section is missing and should be added to summarise key findings, implications, and possible future work.
12. The abbreviation list  is missing.
13. L272, what is S2?
14. In Figure 3, the unit "м/с" is incorrect. It should be "m/s" in Latin characters for consistency with the rest of the manuscript.
15. In Table 1, “Hydrogen consumption” is given as a volumetric flow rate. Since hydrogen is a compressible gas, it would be better to report either mass flow rate or volumetric flow rate with pressure and temperature for clarity and accuracy.

Author Response

We sincerely thank the reviewer for their detailed and constructive feedback. Below we provide point-by-point responses and indicate the changes made in the revised manuscript.

Comment 1: Emphasise the novelty more clearly in the abstract.

Response 1: Agreed. We revised the last two sentences of the abstract to emphasize the novelty more clearly. In addition, a reference to the supporting literature was moved to Line 130 for clarity.

Comment 2: In Line 345 (Methodology section), we read: "The standard k-ε model is the most widely used...". On the other hand, from Line 90 to Line 129, the authors explain several improved versions of the base model (k-ε), as well as some hybrid CFD approaches with improved accuracy and additional features. In other words, if the authors used the standard k-ε model, the Introduction should briefly justify its selection in light of existing alternatives. Alternatively, if the Introduction presents models better than k-ε, the question arises: why was the base model employed?

Response 2: We thank the reviewer for this insightful comment. In the Introduction (Lines 90–129), we provided an overview of advanced turbulence models to demonstrate the range of available tools and contextualize the decision-making process. Despite the existence of more advanced alternatives (e.g., Realizable k-ε, SST k-ω), the standard k-ε model was deliberately selected due to its balance between computational cost and accuracy for the specific geometry and flow conditions of the gas cooler under investigation. Our primary goal was to validate a combined analytical–CFD methodology suitable for practical engineering applications where computational resources may be limited. Moreover, the flow regime in the studied case features high Reynolds numbers and lacks strong separation zones, where the standard k-ε model performs reliably. The justification has been added to the end of the Introduction section.

Comment 3: In Line 110, the phrase “model SST k-ω мод” includes a non-English word ("мод") — this should be corrected.

Response 3: Agreed. The non-English word "мод" has been removed.

Comment 4: In Line 207, the words “Назва параметру Значення” are non-English and should be translated into English (e.g., “Parameter name / Value”).

Response 4: Agreed. The headings in Table 2 have been translated into English accordingly.

Comments 5 & 6: In Table 2 and Line 359, “hight” should be corrected to “height”.

Response 5 & 6: Agreed. Spelling errors have been corrected.

Comment 7: There are incomplete sentences in Lines 248, 251, and 252 — they need revision for grammatical completeness.

Response 7: Agreed. These sentences have been revised for completeness and clarity.

Comment 8: In Figure 5, the x-axis and y-axis labels are unclear. What do "Δt/Δt*" and "*Δt``/Δt" represent? Please clarify.

Response 8: Thank you for the question. Δt represents the temperature difference in counterflow. Δt′ and Δt′′ represent the first and second derivatives of Δt, respectively. These indicate the rate and acceleration of heat transfer intensity with respect to the heat exchange surface area, where ?t=??/??, Q is the heat quantity, and F is the heat exchange surface area.

Comment 9: The colour maps in Figures 11 and 12 are not legible — use more distinguishable colour gradients or annotate the range for clarity.

Response 9: Thank you for the helpful remark. We improved the readability and contrast of the color bars in Figures 11 and 12.

Comment 10: The Discussion section is too brief and does not adequately contextualise or reflect on the findings. It should be expanded.

Response 10: Agreed. The Discussion section has been expanded to include an explanation of how the observed nonuniform temperature distribution may affect further mechanical calculations and structural integrity.

Comment 11: The Conclusion section is missing and should be added to summarise key findings, implications, and possible future work.

Response 11: Thank you. A Conclusion section has been added to the manuscript summarizing key findings and outlining future research directions.

Comment 12: The abbreviation list is missing.

Response 12: We thank the reviewer for this observation. The manuscript uses commonly accepted terms and abbreviations widely known in the fields of heat transfer, fluid dynamics, and CFD modeling (e.g., CFD, Re, Nu, k-ε), which are standard in the scientific literature and well-understood by the target audience of the journal. Therefore, we intentionally refrained from duplicating them in a separate abbreviation list. However, if required by the journal’s editorial policy or upon the reviewers’ request, we are ready to promptly include the list of abbreviations in the final version of the manuscript.

Comment 13: L272, what is S2?

Response 13: S2 refers to the distance between tube rows. This parameter is defined in Table 2 of the manuscript.

Comment 14: In Figure 3, the unit "м/с" is incorrect. It should be "m/s" in Latin characters for consistency with the rest of the manuscript.

Response 14: Agreed. The unit has been corrected to "m/s" in Latin script.

Comment 15: In Table 1, “Hydrogen consumption” is given as a volumetric flow rate. Since hydrogen is a compressible gas, it would be better to report either mass flow rate or volumetric flow rate with pressure and temperature for clarity and accuracy.

Response 15: Thank you for the suggestion. Pressure and temperature values were already included in Table 2. However, we recalculated the hydrogen consumption and added the corresponding mass flow rate to Table 1 for completeness and clarity.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Thanks for the improvements in layout and formatting.
I would like to highlight some key fundamental issues that need further efforts to meet standard academic expectations:

1. In simple words, your research is confined to a CFD analysis of a gas cooler.
   As a pure CFD study, it requires verification from the literature—ideally with comparable-scale gas coolers (in terms of cooling capacity, structure, etc.). If no similar studies exist and verification is not feasible, a clear justification should be included in the manuscript.
2. As a CFD-based work, it needs further support, such as a mesh independence analysis, to ensure the reliability and robustness of the results.
3. Some terminologies used in the manuscript do not sound professional. For example:
   While your work is CFD-based—and CFD is a numerical approach—you state: "This study presents a hybrid analytical–numerical approach." This phrase "hybrid" appears for the first time in the conclusion. Have you conducted both CFD and analytical calculations? If so, please include a comparison to support your outcomes. Otherwise, what is the rationale for being hybrid?
   If the study is purely CFD-based, please refer to it as a numerical approach and avoid calling it a "hybrid analytical–numerical approach."
4. The results (one paragraph only) and discussion section  (one paragraph only) lacks depth. Additional content could include a sensitivity analysis, validation with reference data, or a comparison of model outcomes under varying assumptions.
5. The conclusions are too generic.
   For instance, the statement: "The proposed method allows for accurate estimation" is a strong claim.
   What evidence supports the accuracy of this method? Up to what level of error or discrepancy?
6. Figure 5: The colormap is not legible and should be improved.
7. The parameter name "Adduced ratio" is not common in engineering. Given its unit [kW/(m²·°C)], it is most likely a heat transfer coefficient and should be renamed accordingly.
8. There is a discrepancy between parameter names used in the tables and the text.
   For example, Table 4 includes “Heat transfer coefficient, K” [kW/(m²·°C)], but in line 339 the same unit is used for a parameter named “Heat load of the cooler”, which is misleading.
   Heat load should be expressed in kW, not in W/(m²·°C). This naming inconsistency will confuse readers and must be corrected.
9. Additionally, you have not included a list of abbreviations, which makes it difficult to follow the text. Here I explain an example of confusion: For example, "parameter m" is unclear. In line 278, m is defined as the number of rows, yet in Table 4 m = 69, 94, which is inconsistent. In contrast, Table 2 states: Number of rows in a section, m = 13 pcs; also Number of tubes in a section = 338 pcs. There is a naming clash because “m” is also used in line 291 as "Effective length of gas cooler tubes, m", and in line 292, where m appears again as a unit. Using the same format for parameter symbols and units (e.g., both in plain text) is a source of confusion.
   Please revise the manuscript thoroughly to: A) write all units in [ ] in text, legend, caption, and axis labels. This really helps the reader like the “m” issue. B) Avoid duplication of symbols C) Ensure consistent and unambiguous usage.
10. Some units are incorrect: Line 283: "Loss of gas pressure in the cooler, mm". Obviously, Pressure should not be in millimetres; Line 327: "Water pressure loss in the cooler, m". A unit of metres is not appropriate for pressure loss.
11. Lines 284–285 state guidelines without citations. Please support these values with references.
12. The reported Reynolds number for gas flow (Re ≈ 1080) indicates laminar flow. However, according to literature, internal gas flow becomes turbulent above Re ≈ 2000. Thus, the use of the k-ε turbulence model for gas flow is questionable and needs justification. Alternatively, consider running the CFD with laminar flow for gas and keeping k-ε for liquid flow, if appropriate.
13. As the last point, you discussed a case study of a gas cooler, but I couldn’t find the cooling capacity neither in the abstract nor in the conclusion. For example, if it is a 5 kW gas cooler—like any other heat exchanger—this should be clearly stated.

Comments on the Quality of English Language

 

Author Response

We sincerely thank the reviewer for carefully reading our manuscript and providing valuable feedback. Below we address each comment point-by-point and describe the corresponding revisions.

Comment 1: In simple words, your research is confined to a CFD analysis of a gas cooler.
As a pure CFD study, it requires verification from the literature—ideally with comparable-scale gas coolers (in terms of cooling capacity, structure, etc.). If no similar studies exist and verification is not feasible, a clear justification should be included in the manuscript.

Response 1: Thank you for your valuable comment. The CFD results were verified based on experimental temperature measurements obtained from a working prototype. The deviation between the calculated and experimental temperatures of key elements did not exceed 0.5°C, while the overall model error did not exceed ±1°C. A corresponding clarification has been added to the “Discussion” section.

Comment 2: As a CFD-based work, it needs further support, such as a mesh independence analysis, to ensure the reliability and robustness of the results.

Response 2: Agreed. A sensitivity analysis was performed for a mesh with a base element size of 50mm. Local mesh refinement to 5–10mm was applied in critical areas with fine geometry. The refinement continued until a further 10% reduction in element size did not result in changes in pressure, temperature or velocity of more than 0.1%. This explanation was added to Figures 9 and 10 earlier.

Comment 3: Some terminologies used in the manuscript do not sound professional. For example: While your work is CFD-based—and CFD is a numerical approach—you state: "This study presents a hybrid analytical–numerical approach." This phrase "hybrid" appears for the first time in the conclusion. Have you conducted both CFD and analytical calculations? If so, please include a comparison to support your outcomes. Otherwise, what is the rationale for being hybrid?
If the study is purely CFD-based, please refer to it as a numerical approach and avoid calling it a "hybrid analytical–numerical approach."

Response 3: Thank you for your comments. The term “hybrid” in this study means a combination of analytical determination of the heat transfer coefficient with CFD modeling, in which the pressure losses between the pipes are modeled using a conventional “sponge” zone (porous media). We have made a corresponding explanation in the “Methodology” section (section 2.3), and in the “Conclusions” section we have replaced the term “hybrid” with “combined”.

Comment 4: The results (one paragraph only) and discussion section  (one paragraph only) lacks depth. Additional content could include a sensitivity analysis, validation with reference data, or a comparison of model outcomes under varying assumptions.

Response 4: We appreciate this valuable observation. To enhance the clarity and informativeness of the manuscript, we extended both the Results and Discussion sections. In the Results, we provided a more detailed comparison of calculated thermal parameters and experimental data from an operational prototype. In the Discussion, we elaborated on implications of the local temperature non-uniformity and its potential mechanical consequences, as well as the reliability of the proposed method. The temperature deviation between simulation and experiment did not exceed 0.5°C, confirming the model's accuracy.

Comment 5: The conclusions are too generic. For instance, the statement: "The proposed method allows for accurate estimation" is a strong claim. What evidence supports the accuracy of this method? Up to what level of error or discrepancy?

Response 5: Thank you for pointing this out. We have revised the Conclusion to include quantified evidence supporting the accuracy of the proposed method. Specifically, we clarified that the discrepancy between analytical and CFD results does not exceed 10%, and that simulation results were validated against experimental data with a maximum deviation of ±1°C. These additions substantiate the method's reliability and practical applicability.

Comment 6: Figure 5: The colormap is not legible and should be improved.

Response 6: Thank you. We have changed the title of Figure 5 and added an additional explanation before the figure to improve readability.

Comment 7: The parameter name "Adduced ratio" is not common in engineering. Given its unit [kW/(m²·°C)], it is most likely a heat transfer coefficient and should be renamed accordingly.

Response 7: Agreed. This parameter has been renamed to “Heat transfer coefficient”.

Comment 8: There is a discrepancy between parameter names used in the tables and the text. For example, Table 4 includes “Heat transfer coefficient, K” [kW/(m²·°C)], but in line 339 the same unit is used for a parameter named “Heat load of the cooler”, which is misleading. Heat load should be expressed in kW, not in W/(m²·°C). This naming inconsistency will confuse readers and must be corrected.

Response 8: Thank you for your comment. All parameter names have been reconciled. The designation “K” is now used exclusively for the heat transfer coefficient [kW/(m²·°C)]. Regarding the parameter “Heat load”, the units of measurement [kW/(m²·°C)] are based on the formula, i.e. this is the reduced heat load per unit area.

Comment 9:  Additionally, you have not included a list of abbreviations, which makes it difficult to follow the text. Here I explain an example of confusion: For example, "parameter m" is unclear. In line 278, m is defined as the number of rows, yet in Table 4 m = 69, 94, which is inconsistent. In contrast, Table 2 states: Number of rows in a section, m = 13 pcs; also Number of tubes in a section = 338 pcs. There is a naming clash because “m” is also used in line 291 as "Effective length of gas cooler tubes, m", and in line 292, where m appears again as a unit. Using the same format for parameter symbols and units (e.g., both in plain text) is a source of confusion. Please revise the manuscript thoroughly to: A) write all units in [ ] in text, legend, caption, and axis labels. This really helps the reader like the “m” issue. B) Avoid duplication of symbols C) Ensure consistent and unambiguous usage.

Response 9: Agreed. All units of measurement are now standardized and written in square brackets [ ] in the text, tables, and captions.

Comment 10: Some units are incorrect: Line 283: "Loss of gas pressure in the cooler, mm". Obviously, Pressure should not be in millimetres; Line 327: "Water pressure loss in the cooler, m". A unit of metres is not appropriate for pressure loss.

Response 10: Fixed.

Comment 11: Lines 284–285 state guidelines without citations. Please support these values with references.

Response 11: The recommendations are based on experience in operating and calculating turbogenerator coolers.

Comment 12: The reported Reynolds number for gas flow (Re ≈ 1080) indicates laminar flow. However, according to literature, internal gas flow becomes turbulent above Re ≈ 2000. Thus, the use of the k-ε turbulence model for gas flow is questionable and needs justification. Alternatively, consider running the CFD with laminar flow for gas and keeping k-ε for liquid flow, if appropriate.

Response 12: Thank you for your valid comment. Although the Re value is below the classical limit for turbulence, the design includes special turbulators that artificially generate turbulent flow. For this reason, the laminar simulation does not reflect real conditions. Justification added to the CFD section.

Comment 13: As the last point, you discussed a case study of a gas cooler, but I couldn’t find the cooling capacity neither in the abstract nor in the conclusion. For example, if it is a 5 kW gas cooler—like any other heat exchanger—this should be clearly stated.

Response 13: Thank you. It is specified in the abstract and in the conclusions that the cooling capacity of the studied gas cooler is 3.8 MW (1266 kW for each of the three sections).

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you for all the improvements you have made.  Some additional improvements are still needed, as detailed below:

1 – In response to my previous comment, you mentioned that the results were verified by some experiments. If these experiments have indeed been conducted—this would be valuable research—why are the experimental details not included in the paper? If the experimental results have been published elsewhere by the authors, they must be cited; if not, they should be included in the current manuscript.
Ideally, the following need to be included as a dedicated subsection for the experimental setup:
a) How the experiments were conducted
b) A picture of the experimental setup
c) Boundary conditions
d) Number of experimental tests

In any case, whether the experiments were conducted by the authors or by another researcher, the Results section must include a proper statistical analysis (e.g., to be added in one of the existing figures like Fig. 13), comparing the simulation results with the experimental data.

2 – We read in the revised manuscript, line 438: "The simulation results were validated against experimental measurements from an operational gas cooler prototype." This is definitely not a valid statement. a) What does “an operational gas cooler” mean? An unknown gas cooler by an unknown author? b) "The temperature deviation between simulation and real measurements did not exceed 0.5°C, and the overall discrepancy remained within ±1°C" — this seems very generic and unrealistic. How is it possible that the deviation did not exceed 0.5°C, while the discrepancy (what is the definition of “overall discrepancy”?) is between -1°C and +1°C? These two statements contradict each other. The statistical metrics should be clearly defined, and the data being compared should be presented in a figure or table.

3-Line 166: The phrase “numerical experiment conditions” is unclear. Please clarify whether it refers to the conditions of the numerical simulation, the experimental test, or both.

Author Response

We sincerely thank the reviewer for carefully reading our manuscript and providing valuable feedback. Below we address each comment point-by-point and describe the corresponding revisions.

Comment 1: 

In response to my previous comment, you mentioned that the results were verified by some experiments. If these experiments have indeed been conducted—this would be valuable research—why are the experimental details not included in the paper? If the experimental results have been published elsewhere by the authors, they must be cited; if not, they should be included in the current manuscript.
Ideally, the following need to be included as a dedicated subsection for the experimental setup:
a) How the experiments were conducted
b) A picture of the experimental setup
c) Boundary conditions
d) Number of experimental tests

In any case, whether the experiments were conducted by the authors or by another researcher, the Results section must include a proper statistical analysis (e.g., to be added in one of the existing figures like Fig. 13), comparing the simulation results with the experimental data.

Response 1: 

We appreciate the reviewer’s suggestion to expand the experimental section and statistical validation.

At this stage, we would like to clarify that the experimental validation is based on data obtained by the authors during prior full-scale tests of the hydrogen-cooled turbogenerator TGV-325, under steady-state industrial conditions. These results, including schematics and boundary conditions, are fully documented in the Antona Kovryga PhD thesis and in Bogdan Shestak published conference proceedings.The theses present a workbench (p. 246) and (p. 334), where the parameters of the cooling gas and water are presented, and the dissertation presents a complete scheme for testing turbogenerators (section 4).

To maintain the current structure of the manuscript and avoid excessive expansion, we have chosen to include direct references to these sources in the Results section, where the comparison between simulated and measured thermal parameters is discussed.

Should the editorial board require more detailed integration of the experimental methodology, we are prepared to revise accordingly.

Comment 2: We read in the revised manuscript, line 438: "The simulation results were validated against experimental measurements from an operational gas cooler prototype." This is definitely not a valid statement. a) What does “an operational gas cooler” mean? An unknown gas cooler by an unknown author? b) "The temperature deviation between simulation and real measurements did not exceed 0.5°C, and the overall discrepancy remained within ±1°C" — this seems very generic and unrealistic. How is it possible that the deviation did not exceed 0.5°C, while the discrepancy (what is the definition of “overall discrepancy”?) is between -1°C and +1°C? These two statements contradict each other. The statistical metrics should be clearly defined, and the data being compared should be presented in a figure or table.

Response 2:

Thank you for the important clarification.

In the revised version, the phrase “operational gas cooler prototype” has been replaced with a more accurate description. The validation was conducted using data from stand-based tests of the full-scale hydrogen-cooled turbogenerator TGV-325. These tests were carried out under steady-state conditions, where all key thermal and flow parameters remained stable over extended periods. As a result, traditional statistical sampling was not applied, since industrial regulations require minimal parameter deviation and high reproducibility during such commissioning tests.

Comment 3: Line 166: The phrase “numerical experiment conditions” is unclear. Please clarify whether it refers to the conditions of the numerical simulation, the experimental test, or both.

Response 3:  

Thank you for pointing this out. The phrase “numerical experiment conditions” refers exclusively to the boundary conditions and assumptions used in the CFD modeling. To avoid ambiguity, the sentence has been revised accordingly.