Numerical Analysis of Heat Transfer Behaviours of Melting Process for Ice Thermal Storage Based on Various Heat Source Configurations

Round 1

Reviewer 1 Report

Sustainability

Manuscript Number: - sustainability-2046136

Title: Numerical analysis on heat transfer behaviours of melting process for ice thermal storage based on various heat source configurations

Reviewer report

In this paper, melting performance of PCM in a shell-and-tube latent heat storage (STLHS) unit is numerically studied by considering natural convection in terms of various heat source positions and configurations as central position, eccentric position, and flat-type type. The subject of this paper is important; however, it needs minor revision: 

1-      Authors should show any special novelty in the work.

2-      More aspects relating the practical applicability of the work are recommended to be included in the manuscript.

3-      References for the equations (1)-(5) should be added.

4-      More details for the numerical method should be added.

5-      Authors should revise the English language of whole manuscript.

6-      The conclusion should be revised, improved, and rephrased.

Author Response

storage (STLHS) unit is numerically studied by considering natural convection in terms of various heat source positions and configurations as central position, eccentric position, and flat-type type. The subject of this paper is important; however, it needs minor revision:

• Authors should show any special novelty in the work.
• Thank you very much for your comments. To further state the novelty of this work, we list a table that shows a comparison between this work and some representative literature as follows. It is worth noting that the melting process of ice under the constant heat flux when considering the density inversion has not been studied before. To fill this research gap, the melting process of ice is numerically investigated by constant heat source input in this work. The effects of heat source eccentric and configuration are also presented. The result can provide helpful guides and insights when designing ice thermal storage system and choosing appropriate working conditions.
• Table 1. Comparison between this work with related literature.

2-      More aspects relating the practical applicability of the work are recommended to be included in the manuscript.

• Thank you very much for your comments. More aspects for real application are summarized in the revised version after conclusion which is related with air conditioning system for the mismatch between energy supply and energy demand.
  
  

3-      References for the equations (1)-(5) should be added.

• Thank you very much for your comments. Reference for equations 1-5 is added in the revised work.
  
  

4-      More details for the numerical method should be added.

• Thank you for your comments. We have added the numerical method details in the revised manuscript.
  
  

5-      Authors should revise the English language of whole manuscript.

• Thank you for your comments. All the authors have checked the language carefully. Hope it could meet the standard of the journal this time. The introduction part is greatly revised.
  
  

6-      The conclusion should be revised, improved, and rephrased.

Thank you for your suggestion. The conclustion has been revised to be more concise which aims to illustrate the main contribution of this work.

Author Response File: Author Response.pdf

Reviewer 2 Report

The melting performance of PCM in shell and tube latent heat storage (STLHS) was studied numerically in this paper. The influence of natural convection under different heat source locations and configurations was considered. The temperature distribution, melting time and overall heat transfer coefficient in the melting process were studied. The author drew many useful conclusions from his work.

comments in the article:

1) The language needs to be improved, some typos and grammar mistakes are found in the paper;

2) The format of the reference is inconsistent in the text, for example, the superscript is used when 31,31 is quoted on page 5. Please check it carefully;

3) The areas indicated in purple in Figure 5b are not consistent with the local diagram shown in the upper right corner;

4) Please explain why the melting times in Figure 7 and Figure 8 are different. Figures 10 and 11 have the same problems;

5) The first sentence in the Conclusions “This section is not mandatory but can be added to the manuscript if the discussion is unusually long or complex.” can be deleted;

6) In Conclusion 1, the higher the heat flux, the shorter the melting time should be. Why “The melting time of PCM with a heat flux of 3000 W· m-2 is more than 5 times longer than that of PCM with a heat flux of 500 W· m-2.” In addition, please further explain why the direction of heat convection changes with the different heat flux;

7) In my opinion, the author should further refine the conclusions presented in the paper rather than simply summarize the physical phenomena obtained. It should be explained in the light of the author's knowledge to show the depth of the paper.

Author Response

Reviewer #2: The melting performance of PCM in shell and tube latent heat storage (STLHS) was studied numerically in this paper. The influence of natural convection under different heat source locations and configurations was considered. The temperature distribution, melting time and overall heat transfer coefficient in the melting process were studied. The author drew many useful conclusions from his work.

comments in the article:

1) The language needs to be improved, some typos and grammar mistakes are found in the paper;

• Thank you for your good suggestion. All the authors have checked the language carefully. Hope it could meet the standard of the journal this time. The introduction part is greatly revised.
  
  

2) The format of the reference is inconsistent in the text, for example, the superscript is used when 31, 31 is quoted on page 5. Please check it carefully;

• Thank you very much for your comments. We have rechecked the format of reference to ensure the correctness of the revised manuscript.

3) The areas indicated in purple in Figure 5b are not consistent with the local diagram shown in the upper right corner;

• Thank you very much for your comments. We have updated the figure. Areas indicated in purple in Figure 5b are consistent with the local diagram in the revised manuscript which is as follows:
• “ ”

4) Please explain why the melting times in Figure 7 and Figure 8 are different. Figures 10 and 11 have the same problems;

• Thank you very much for your comments. When total input heat power is fixed, e.g. 500 W·m^-2 in Figure 7, the sum of sensible heat storage power and latent heat storage power is fixed. But under different heat source configurations, the heat transfer performance is different. The high heat transfer coefficient means a smaller heat transfer difference between heat source temperature and melting temperature, leading to a lower temperature of liquid PCM. That means the sensible heat storage power is relatively small, and the latent heat storage power is higher. Further, the solid PCM can be melted in a shorter time. In Figures 7 and 8, the heat sources are located in different places and the heat transfer performance for each case is different. Thus, the melting times in Figure 7 and Figure 8 are different. The differences in Figures 10 and 11 are caused by the same reason.

5) The first sentence in the Conclusions “This section is not mandatory but can be added to the manuscript if the discussion is unusually long or complex.” can be deleted;

• Thank you very much for your comments. The sentence has been deleted and the whole conclusion is revised to be more concise.

6) In Conclusion 1, the higher the heat flux, the shorter the melting time should be. Why “The melting time of PCM with a heat flux of 3000 W· m-2 is more than 5 times longer than that of PCM with a heat flux of 500 W· m-2.” In addition, please further explain why the direction of heat convection changes with the different heat flux;

• Thank you very much for your comments. We feel very sorry for the writing mistake. The right version should be “The melting time of PCM with a heat flux of 500 W·m^-2 is more than 5 times longer than that of PCM with a heat flux of 3000 W·m^-2.” We have corrected it in the revised manuscript.
• The reason for the influence of heat flux on convection direction is listed as follows: “Water has a unique density characteristic that it increases with the increase of temperature when temperature is lower than 277.15 K, while it decreases with the increase of temperature when temperature is higher than 277.15 K. The density under 277.15 K reaches the maximum. Owing to this feature, the hot water moves downwards when temperature is lower than 277.15 K and moves upwards when temperature is higher than 277.15 K. For different heat flux, the temperature of liquid water is different. When heat flux is relatively small, e.g. 500 W·m^-2, the water temperature is mainly in the range of 273.1 K to 277.15 K. While when heat flux is relatively large, e.g. 3000 W·m^-2, the water temperature is always higher than 277.15 K. Thus, the natural convection directions of this two conditions are different. That means the direction of heat convection changes with the different heat flux.

7) In my opinion, the author should further refine the conclusions presented in the paper rather than simply summarize the physical phenomena obtained. It should be explained in the light of the author's knowledge to show the depth of the paper.

• Thank you very much for your suggestion. The conclusion is revised to be more concise. Also the the main contribution and depth of the paper is illustrated in light of the author’s knowledge.

Author Response File: Author Response.pdf

Reviewer 3 Report

This manuscript conducts a numerical analysis of the melting process for three configurations: central position, eccentric position, and flat-tube configurations. This is an incremental work that is based on the authors’ previous research to model the effect of natural convection. The topic can be of interest to the readers.  However, this paper in its current form does not include enough details on the computational method and basic assumptions. Below are the issues that need to be addressed before this manuscript can be considered for publication.

1.       The method section should be described in the past tense.

2.       The authors use the enthalpy-porosity method by Brent et al. to model the phase change system (Eq. 5). This is a critical assumption and needs to be included in the “pertinent assumption” list. Discussion on how accurate this model applies to ice-water systems and relevant references need to be included.

3.       The physical meaning of the liquefaction rate needs to be explained explicitly.

4.       In Figure 5a (same for Figure 6a, 10a), Is the liquefaction rate (0.1 to 0.9) a local or global constant?

5.       More details on the model calibration (line 192-196) needs to be included. I understand that there is more description in the authors’ previous work, but it is much easier on the readers if a general description is provided here.

6.       Line 343. “This section is not mandatory but can be added to the manuscript if the discussion is 344 unusually long or complex” should not appear in the manuscript.

Author Response

Reviewer #3: This manuscript conducts a numerical analysis of the melting process for three configurations: central position, eccentric position, and flat-tube configurations. This is an incremental work that is based on the authors’ previous research to model the effect of natural convection. The topic can be of interest to the readers.  However, this paper in its current form does not include enough details on the computational method and basic assumptions. Below are the issues that need to be addressed before this manuscript can be considered for publication.

1. The method section should be described in the past tense.

• Thank you for your good suggestion. We have modified the tense in method section in the revised manuscript.

2. The authors use the enthalpy-porosity method by Brent et al.to model the phase change system (Eq. 5). This is a critical assumption and needs to be included in the “pertinent assumption” list. Discussion on how accurate this model applies to ice-water systems and relevant references need to be included.

• Thank you for your good suggestion. We have added it to the “pertinent assumption” list in the revised manuscript. Enthalpy-porosity is a common method to simulate the phase change process of the PCM. It has been successfully applied in various kinds of PCM in the open literature, including pure gallium [1], paraffin wax [2], hydrated salts [3]. More specifically, the accuracy of this method on the melting process of ice-water systems is also well verified in the references [4, 5]. Thus, we consider that the enthalpy-porosity method is suitable for the simulation in this work.
• Reference:
• [1] Brent A D, Voller V R, Reid K T J. Enthalpy-porosity technique for modeling convection-diffusion phase change: application to the melting of a pure metal[J]. Numerical Heat Transfer, Part A Applications, 1988, 13(3): 297-318.
• [2] Chakraborty P R. Enthalpy porosity model for melting and solidification of pure-substances with large difference in phase specific heats[J]. International Communications in Heat and Mass Transfer, 2017, 81: 183-189.
• [3] Younsi Z, Naji H. A numerical investigation of melting phase change process via the enthalpy-porosity approach: Application to hydrated salts[J]. International Communications in Heat and Mass Transfer, 2017, 86: 12-24.
• [4] Niezgoda-Żelasko B. The enthalpy-porosity method applied to the modelling of the ice slurry melting process during tube flow[J]. Procedia Engineering, 2016, 157: 114-121.
• [5] Wu F, Fan YB, Zhang XJ, Zhang H, Wang ZL, Wang ZW, et al. Performance prediction on ice melting process for cold energy utilization: Effect of natural convection. Journal of Energy Storage. 2022;55:105638.

3. The physical meaning of the liquefaction rate needs to be explained explicitly.

• Thank you for your good suggestion. Liquefaction rate is a constant which represent the proportion of liquid PCM in total PCM. It is 1 for liquid PCM and 0 for solid PCM. We have added a clearer explanation of liquefaction rate in revised manuscript.

4. In Figure 5a (same for Figure 6a, 10a), Is the liquefaction rate (0.1 to 0.9) a local or global constant?

• Thank you for your good question. The liquefaction rate in Figure 5a (same for Figure 6a, 10a) is the global constant. Figure 5a shows the melting evolutions of PCM in terms of different heat flux from 500 W·m^-2 to 3000 W·m^-2 and liquefaction rate distribution when the global average liquefaction rate increases from 0.1 to 0.9. We have cleared the descriptions in the revised manuscript.

5. More details on the model calibration (line 192-196) needs to be included. I understand that there is more description in the authors’ previous work, but it is much easier on the readers if a general description is provided here.

• Thank you for your good suggestion. We have added more details about the model calibration in the revised manuscript, including the independence validations of tine step and mesh grids.

6. Line 343. “This section is not mandatory but can be added to the manuscript if the discussion is 344 unusually long or complex” should not appear in the manuscript.

• Thank you for your good suggestion. We have deleted it in the revised manuscript.

Author Response File: Author Response.pdf