Steady-State Feasibility of a Phase Change Material-Based Defrosting System and Energy Storage Management Strategies

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript proposes a phase change material-based defrosting system (PCM-DS) integrated into a vapor compression refrigeration system (VCRS), aiming to utilize compressor waste heat for defrosting. A steady-state thermodynamic model is developed and three energy storage management strategies are compared. The study is supported by experimental data used as boundary conditions.The manuscript is generally well structured, and the idea of integrating PCM for defrosting is interesting from an engineering perspective.

However, the following issues still deserve further consideration:

1. The present study employs a steady-state thermodynamic model to analyze the PCM-based defrosting process. However, the actual defrosting process involves inherently transient heat transfer and phase change phenomena. It is recommended that the authors clarify the applicability and limitations of the steady-state model, or include a discussion on transient effects to enhance the credibility of the results.
2. The analysis of the PCM system is currently based mainly on theoretical modeling, with a lack of experimental validation or comparison with existing studies. The authors are encouraged to provide validation (e.g., experimental data or comparison with literature) to support the reliability of the model predictions.
3. The manuscript compares the COP of PCM-based defrosting with that of electric heater defrosting. However, the two methods differ in terms of energy sources and system boundaries. It is recommended that the authors clearly define the COP calculation boundary and discuss the fairness of this comparison to improve the rigor of the conclusions.
4. One of the conclusions states that the unique superheating energy storage management strategy is advantageous, but this is mainly supported by qualitative description. It is recommended to include quantitative comparisons (e.g., in tabular or graphical form) among the three strategies to more clearly demonstrate their engineering performance and strengthen the reliability of the conclusion.

Author Response

The authors thank the reviewer for the time taken to read and evaluate the paper. The comments have been taken into consideration. Each comment has been addressed individually, and the modification has been highlighted in text in green. The authors consider that the reviewer’s comments are important and the paper is better structured and the work is better pointed out.

Comment 1: The present study employs a steady-state thermodynamic model to analyze the PCM-based defrosting process. However, the actual defrosting process involves inherently transient heat transfer and phase change phenomena. It is recommended that the authors clarify the applicability and limitations of the steady-state model or include a discussion on transient effects to enhance the credibility of the results.

 

Response 1: This comment is appreciated as it points out better the goal of the work. A comment regarding the limitations and applicability of the steady-state modelling and the involvement in future work of transient heat transfer phenomena, moving boundary between liquid and solid PCM, PCM behavior during phase-change and convective currents has been added in Section 2, after Table 1, highlighted in green. (Lines 188-207)

Comment 2: The analysis of the PCM system is currently based mainly on theoretical modeling, with a lack of experimental validation or comparison with existing studies. The authors are encouraged to provide validation (e.g., experimental data or comparison with literature) to support the reliability of the model predictions.

Response 2: The suggestion of the reviewer is very good. The authors have inserted validation section 2.4. The numbers of papers published in the field of PCM-DS for refrigeration systems and not heat pumps are limited. Nevertheless, the authors have found related but not similar work in references [17] and [19].  Validation Section 2.4 has been added in Section 2, after 2.3 Uncertainty Analysis section and is highlighted in green (Lines 390-409).

Comment 3: The manuscript compares the COP of PCM-based defrosting with that of electric heater defrosting. However, the two methods differ in terms of energy sources and system boundaries. It is recommended that the authors clearly define the COP calculation boundary and discuss the fairness of this comparison to improve the rigor of the conclusions.

Response 3: The authors appreciate this comment. In section 3 Result and Discussion, after Figure 11, the phrase :” In case of using the EHD, present on the experimental setup, the COP is 19% lower than the COP of the VCRS without PCM-DS. One can notice a consistent difference between the COP of the VCRS with PCM-DS and the one with EHD.” has been replaced with the one highlighted in green (Lines 478-484). It is not necessarily wrong to compute the COP with the real power of the electrical resistance mounted on the experimental setup but as the reviewer mentioned, it is indeed not fair. The authors corrected this approach.

Comment 4: One of the conclusions states that the unique superheating energy storage management strategy is advantageous, but this is mainly supported by qualitative description. It is recommended to include quantitative comparisons (e.g., in tabular or graphical form) among the three strategies to more clearly demonstrate their engineering performance and strengthen the reliability of the conclusion.

Response 4: The request of the reviewer has been fulfilled. A comparative table between the three management strategies has been introduced in section 3 as Table. 7. Comments and discussion have been added and are highlighted in green. Due to this welcome change, Figure 1 has been also changed by adding 4 solenoid valves. The energy consumption of the solenoid valves has been used to evaluate a COP value for each management strategy and also, comments about operation details have been added for each management strategy after Figures 12, 13 and 14. All these modifications are highlighted also in green.

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents a promising concept, but it should be revised to clearly reflect its preliminary theoretical nature, improve model transparency, and provide stronger justification of assumptions and performance claims.
1. The title should be revised because the study is primarily a theoretical, steady-state feasibility analysis rather than a fully experimentally validated performance study.
2. The abstract should clearly state that the PCM-based defrosting system was modelled, not experimentally installed or tested.
3. The novelty claim should be softened. PCM- and TES-based defrosting have already been reported in previous studies, so the main novelty should focus on comparing the three proposed energy-storage management strategies.
4. The experimental section needs more detail. Important frost-formation parameters, such as relative humidity, vapour generation rate, air velocity, evapourator surface temperature, and the repeatability of 1 kg ice formation, should be reported.
5. The heat-loss model must be fully described. The manuscript mentions heat loss from the PCM-Hx, but it does not provide the equations, assumptions, geometry, convective heat transfer coefficient, or boundary conditions.
6. Several model assumptions are too idealized and require justification or sensitivity analysis, especially isentropic compression, constant condensing temperature, saturated refrigerant states, fixed pressure drop, and constant PCM phase-change temperatures.
7. The COP comparison is too optimistic. The PCM-DS COP primarily accounts for pump energy, whereas real penalties such as valve losses, added pressure drop, control system losses, extra refrigerant charge, and heat-transfer limitations are not fully accounted for.
8. The reported COP benefit should be described as theoretical feasibility, not as proof of practical performance.
9. The three energy storage strategies should be compared in a dedicated table, including control complexity, number of additional components, risk of incomplete defrosting, energy penalty, reliability, cost, and PCM degradation risk.
10. The intermittent bypass strategy needs clearer discussion because it may not always store enough energy to fully melt 1 kg of ice.
11. The PCM degradation discussion should be softened. The estimated 167-day degradation period is only a rough theoretical estimate and should not be presented as a confirmed replacement time.
12. The uncertainty analysis should be expanded to include uncertainty in PCM properties, heat loss coefficient, compressor parameters, pressure drop, and thermodynamic property calculations.
13. The selection of OM42 should be better justified, especially since its flammability is marked as “Yes” in the PCM properties table.
14. Figures need improvement, especially font size, legends, axis labels, units, and caption clarity.
15. Notation and terminology should be made consistent. For example, “heat flux” should be replaced with “heat rate” where appropriate, and symbols for mass and mass flow rate should not be confused.
16. The conclusion should be shortened and restructured into key findings, limitations, and future work.
17. The language requires careful editing to correct grammar, unclear phrasing, and typographical errors throughout the manuscript.

Author Response

The authors would like to express sincere gratitude for the reviewer’s valuable time and constructive comments on the manuscript. We have carefully considered all the suggestions and revised the paper accordingly. Now, the paper is better structured, and the work has been considerably improved.

Comment 1: The title should be revised because the study is primarily a theoretical, steady-state feasibility analysis rather than a fully experimentally validated performance study.

Response 1: The authors have taken into consideration the suggestion. Indeed, performance has to be related not only to theoretical analysis but also to experimental analysis. The title has been changed from “Steady-state performance of a phase change material-based defrosting system and energy storage management strategies “to “Steady-state feasibility analysis of a phase change material-based defrosting system and energy storage management strategies”.

Comment 2: The abstract should clearly state that the PCM-based defrosting system was modelled, not experimentally installed or tested.

Response 2: Following this suggestion, the abstract has been modified by adding the following: “The PCM-DS is not installed on the experimental setup. The latter is used to obtain experimental data to be used as inputs in the steady-state model.” The modification is highlighted in blue.

Comment 3: The novelty claim should be softened. PCM- and TES-based defrosting have already been reported in previous studies, so the main novelty should focus on comparing the three proposed energy-storage management strategies.

Response 3: The authors understand the suggestion. The word “novelty” was deleted from the beginning of the abstract and it was stated that the core innovation is related to the three proposed energy-storage management strategies.

Comment 4: The experimental section needs more detail. Important frost-formation parameters, such as relative humidity, vapour generation rate, air velocity, evapourator surface temperature, and the repeatability of 1 kg ice formation, should be reported.

Response 4: The experimental section has been improved. In terms of frost formation parameters, in the paper it is mentioned that the relative humidity has not been recorded. The vapor generation rate is 0.08 g/s and a comment highlighted in blue has been added in section 2.1 (Lines 125-126). The air velocity in the cold room has not been recorded. A comment regarding this subject has been added in section 2.1 highlighted in blue (Line 131). The evaporator surface temperature has been recorded and a plot showing its variation has been added in the paper in section 2.1 as Fig. 3b). A comment regarding the evolution of the evaporator surface temperature has been added in the same section and is highlighted in blue (Lines 134-135).

Comment 5: The heat-loss model must be fully described. The manuscript mentions heat loss from the PCM-Hx, but it does not provide the equations, assumptions, geometry, convective heat transfer coefficient, or boundary conditions.

Response 5: The heat-loss model was described. The equations, assumptions, geometry, convective heat transfer coefficient and boundary conditions were provided in Section 2.2, Lines (288-305).

Comment 6: Several model assumptions are too idealized and require justification or sensitivity analysis, especially isentropic compression, constant condensing temperature, saturated refrigerant states, fixed pressure drop, and constant PCM phase-change temperatures.

Response 6: The reviewer’s suggestion has been taken into consideration. For the mentioned assumptions, justification has been provided under Table 1 (Lines 169-182) and at the top of Figure 5 (Lines 160-161) and is highlighted in blue.

Comment 7: The COP comparison is too optimistic. The PCM-DS COP primarily accounts for pump energy, whereas real penalties such as valve losses, added pressure drop, control system losses, extra refrigerant charge, and heat-transfer limitations are not fully accounted for.

Response 7: This is a valuable and pertinent observation. The authors have added a comment in section 3 under Fig. 11 highlighted in blue regarding this recommendation (Lines 473-478). It is right that the 3% difference between the COP of the VCRS without PCM-DS and COP of the VCRS with PCM-DS is optimistic. The reason why the authors have not considered the valve losses, added pressure drop, control system losses, extra refrigerant charge, and heat-transfer limitations is because at this moment of the work, the authors don’t know the real size of the future experimental PCM-DS setup.

Comment 8: The reported COP benefit should be described as theoretical feasibility, not as proof of practical performance.

Response 8: This comment has been taken into consideration, and “practical benefit” have been replaced with “theoretical feasibility” and can be seen highlighted in blue in section 3 under Fig. 11  (Line 485). This theoretical feasibility is supported by a paragraph added before at the recommendations of reviewer 1. In this comment, the ideal case for EHD is compared with the ideal case of PCM-DS in terms of theoretical COP. The theoretical COP for EHD is 2.8 and the theoretical COP for the PCM-DS is 3.02 (Lines 478-484).

Comment 9: The three energy storage strategies should be compared in a dedicated table, including control complexity, number of additional components, risk of incomplete defrosting, energy penalty, reliability, cost, and PCM degradation risk.

Response 9: This recommendation has been taken in consideration, and Table 7 was added in section 3 and the information in the table is part of the reviewer’s recommendation that can be evaluated at this stage of the work. Problems regarding the cost, reliability and incomplete defrosting are difficult to be evaluated in this theoretical stage and will be evaluated in a future work where the experimental setup will be developed. Table 7 has been also commented between lines 581 and 606.

Comment 10: The intermittent bypass strategy needs clearer discussion because it may not always store enough energy to fully melt 1 kg of ice.

Response 10: In order to address this recommendation of the reviewer, a comment regarding the limitations of the intermittent bypass management strategy is added in section 3 below Table 7 and is highlighted in blue (Lines 585-587).

Comment 11: The PCM degradation discussion should be softened. The estimated 167-day degradation period is only a rough theoretical estimate and should not be presented as a confirmed replacement time.

Response 11: The reviewer is right. This recommendation is very good and a comment on the reviewer’s suggestion has been added in section 3 right before Table 7 and is highlighted in blue (Lines 577-578).

Comment 12: The uncertainty analysis should be expanded to include uncertainty in PCM properties, heat loss coefficient, compressor parameters, pressure drop, and thermodynamic property calculations.

Response 12: The uncertainty analysis has been completed with comments regarding the absolute uncertainties for PCM properties, heat loss coefficient, compressor parameters, pressure drop, and thermodynamic property calculations. The added comments can be seen at the bottom of Table 4 and are highlighted in blue (Lines 378-383).

Comment 13: The selection of OM42 should be better justified, especially since its flammability is marked as “Yes” in the PCM properties table.

Response 13: A comment regarding the reviewer’s suggestion has been added in section 3 below Table 6 and is highlighted in blue (Lines 431-433).

Comment 14: Figures need improvement, especially font size, legends, axis labels, units, and caption clarity.

Response 14: The quality of the figures has been improved and the captions modified for a better understanding.

Comment 15: Notation and terminology should be made consistent. For example, “heat flux” should be replaced with “heat rate” where appropriate, and symbols for mass and mass flow rate should not be confused.

Response 15: The terms “heat flux” were replaced with “heat rate” and also mass and mass flow rate confusions have been checked.

Comment 16. The conclusion should be shortened and restructured into key findings, limitations, and future work.

Response 16: The conclusions section has been shortened and the key findings rewritten. Also, limitations and future work were mentioned.

Comment 17. The language requires careful editing to correct grammar, unclear phrasing, and typographical errors throughout the manuscript.

Response 17:  The manuscript has been checked once more English grammar, unclear phrasing, and typographical errors. The authors have done their best to correct the errors.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The author has addressed my comments, and the manuscript now meets the requirements for publication.

Reviewer 2 Report

Comments and Suggestions for Authors

This work can be accepted for publication in the present modified version.