Calculation of the Optimal Magnetic Duty Cycle for a Graded Coaxial Magnet of a Rotary Type Magnetic Refrigerator^†

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

            The paper entitled “Calculation of the Optimal Magnetic Duty Cycle for a Coaxial Magnet of a Rotary-Type Magnetic Refrigerator” presents a numerical simulation analysis of a coaxial magnet designed using the COMSOL program for a rotary-type active magnetic refrigeration (AMR) system. The study uses gadolinium (Gd) as the magnetocaloric material, designed as thin sheets with coolant flowing through the gaps between the sheets, and a cylindrical magnet with a stationary outer iron yoke and a rotating inner pole. The authors focus on optimizing the magnetic duty cycle, aiming to achieve the best cooling performance and efficiency of the system. This is done through numerical 3D calculations of the magnetic field, investigating the magnetic field distribution and the thermal-hydraulic performance of the system under different duty cycles.

           The topic is relevant to the field of magnetic refrigeration, addressing a critical aspect of optimizing cooling efficiency. The study employs a numerical simulations approach, providing detailed analysis and validation. The findings have practical implications for the design and optimization of magnetic refrigeration systems, potentially leading to more efficient and cost-effective solutions.

          The text needs a general revision to improve a few parts. Some sentences are long and complex, making the text difficult to read. Some phrases can be made clearer, including grammar and punctuation. However, overall, the article presents valuable research and is a strong candidate for publication with some minor revisions.

          As examples, here are some parts that need attention:

- Lines 25 and 26: "Magnetic Refrigeration (MR) at room temperature is a good alternative to replace a gas compression refrigeration system". MR can potentially promise refrigeration devices, but there are still several challenges, and it is not accurate to say this is a good alternative yet, as the text cites later.

- Line 37: The material is "expensive," not "expansive."

- Line 97: The definition of phi and the arc of phi is unclear. The angle phi is not visible enough in Figure 1.

- Figure 2 can be more enlightening and explanatory if the vector field is included. Additionally, Figure 3 can have better visual quality. Actually, all the figures should maintain the same standard (fonts, size etc.).

- Line 166: The “duty cycle” expression needs a better definition, i.e., the time that the material is magnetized/demagnetized. In fact, Section 4, Results and Discussions, can be more comprehensible by defining a starting point in Figures 1 and 2, linking to magnetic field distribution figures. In addition, some expressions can be defined in order to clarify the explanation and the analysis of the system.

Comments on the Quality of English Language

Overall, the text is well written. However, section 4, Results and Discussions, needs to be improved to better understand the work.

Author Response

Reply to Reviewer1

 

The paper entitled “Calculation of the Optimal Magnetic Duty Cycle for a Coaxial Magnet of a Rotary-Type Magnetic Refrigerator” presents a numerical simulation analysis of a coaxial magnet designed using the COMSOL program for a rotary-type active magnetic refrigeration (AMR) system. The study uses gadolinium (Gd) as the magneto caloric material, designed as thin sheets with coolant flowing through the gaps between the sheets, and a cylindrical magnet with a stationary outer iron yoke and a rotating inner pole. The authors focus on optimizing the magnetic duty cycle, aiming to achieve the best cooling performance and efficiency of the system. This is done through numerical 3D calculations of the magnetic field, investigating the magnetic field distribution and the thermal-hydraulic performance of the system under different duty cycles.

 

           The topic is relevant to the field of magnetic refrigeration, addressing a critical aspect of optimizing cooling efficiency. The study employs a numerical simulations approach, providing detailed analysis and validation. The findings have practical implications for the design and optimization of magnetic refrigeration systems, potentially leading to more efficient and cost-effective solutions.

 

 

Reply: Thanks to the positive confirmation of the reviewer.

 

          The text needs a general revision to improve a few parts. Some sentences are long and complex, making the text difficult to read. Some phrases can be made clearer, including grammar and punctuation. However, overall, the article presents valuable research and is a strong candidate for publication with some minor revisions.

 

          As examples, here are some parts that need attention:

 

- Lines 25 and 26: "Magnetic Refrigeration (MR) at room temperature is a good alternative to replace a gas compression refrigeration system". MR can potentially promise refrigeration devices, but there are still several challenges, and it is not accurate to say this is a good alternative yet, as the text cites later.

Reply: Thanks the suggestion of the reviewer. The sentence: “Magnetic Refrigeration (MR) at room temperature is a good alternative to replace a gas compression refrigeration system” was rewritten into a more conservative word: “Magnetic Refrigeration (MR) at room temperature could be a good alternative to replace a gas compression refrigeration system”.

 

- Line 37: The material is "expensive," not "expansive."

Reply: Sorry about this typo. It was corrected in text (see introduction).

 

- Line 97: The definition of phi and the arc of phi is unclear. The angle phi is not visible enough in Figure 1.

Reply: The phi angle is the angle of between the two interface planes of NdFeB magnets and pole faces. We add this definition to the text. We also made modification of Figure 1 to make it clear.

 

- Figure 2 can be more enlightening and explanatory if the vector field is included. Additionally, Figure 3 can have better visual quality. Actually, all the figures should maintain the same standard (fonts, size etc.).

Reply: Thanks to the suggestion of the reviewer. A vector field view was added to the Fig. 2(b) 

 

- Line 166: The “duty cycle” expression needs a better definition, i.e., the time that the material is magnetized/demagnetized. In fact, Section 4, Results and Discussions, can be more comprehensible by defining a starting point in Figures 1 and 2, linking to magnetic field distribution figures. In addition, some expressions can be defined in order to clarify the explanation and the analysis of the system.

Reply: Thanks the suggestion of the reviewer. Since Fig. 1 and Fig. 2 are the two cross section view of a cylindrical rotary refrigerator in two fold symmetry, the magnetic cycle time of one revolution corresponds to the 0-180 and 180-360 degrees. In the configuration of Fig. 1 and Fig. 2, the pole piece is also in two-fold symmetry, therefore, the magnetic field between the gap of rotor and stator (yoke) is in 180 degrees, two-fold symmetry. We define the magnetic duty cycle when the angle interval (or time interval) magnetic field reaches more 90% of peak magnetic field of each magnetization cycle, which rotates 180 degrees.  

 

 

Comments on the Quality of English Language

Overall, the text is well written. However, section 4, Results and Discussions, needs to be improved to better understand the work.

Reply: Thanks the suggestion of the reviewer. The manuscript of section 4 was substantially revised into section 4-1: Optimize the magnetic duty cycle and section 4.2 for graded magnet arrangement along the axial direction.

 

 

Reviewer 2 Report

Comments and Suggestions for Authors

After a careful reading of the manuscript, I must conclude that it cannot be published in its current form. Below is a list of questions and comments that will help to improve the quality of the manuscript.

1. The article completely lacks a description of the heat transfer modelling, whereas the simulation of the AMR cycle is an extremely complex task. For example, you can refer to one of the recent works that considers an approach to modelling this cycle "Karpenkov, A., Tukmakova, A., Dunaeva, G., Dergachev, P., & Karpenkov, D. (2024). Simulation of the operation of nested Halbach cylinder arrays in regenerative magnetic cooling cycles: The way to the maximum thermal span. International Journal of Refrigeration, 168, 29-39". 

2. Since the optimisation of the magnetic system is based on maximising the cooling capacity, it is necessary to take into account the synchronization of the processes of pumping the heat transfer fluid and introducing the magnetic field. In addition, the cooling capacity is influenced by the geometry of the heat exchanger, the optimisation of which is a separate task that is not discussed in this article.

3. Do the authors of the article consider the variation of the rotor speed, which can be achieved using a stepper motor? This variation can significantly affect the dute cycle.

Author Response

Reply to reviewer 2

 

 

After a careful reading of the manuscript, I must conclude that it cannot be published in its current form. Below is a list of questions and comments that will help to improve the quality of the manuscript.

 

1. The article completely lacks a description of the heat transfer modelling, whereas the simulation of the AMR cycle is an extremely complex task. For example, you can refer to one of the recent works that considers an approach to modelling this cycle "Karpenkov, A., Tukmakova, A., Dunaeva, G., Dergachev, P., & Karpenkov, D. (2024). Simulation of the operation of nested Halbach cylinder arrays in regenerative magnetic cooling cycles: The way to the maximum thermal span. International Journal of Refrigeration, 168, 29-39".

Reply: Thanks the suggestion of the reviewer. We already referred this updated paper and cited this newly published paper (2024) into the revised manuscript. However, the Halbach configuration is different from our two-pole rotary model. In order to expand thermal span of MR using Halbach cylinder arrays, we adapt the concept of graded magnetic along the flow direction, which is reported in this revised manuscript. In addition, in this manuscript, we intent not to write the heat transfer model in detail, because we are only emphasized on the optimization of the magnetic configuration. For detailed heat transfer model, the reader can refer to the reference cited in our manuscript.

 

2. Since the optimisation of the magnetic system is based on maximising the cooling capacity, it is necessary to take into account the synchronization of the processes of pumping the heat transfer fluid and introducing the magnetic field. In addition, the cooling capacity is influenced by the geometry of the heat exchanger, the optimisation of which is a separate task that is not discussed in this article.

Reply: Thanks the suggestion of the reviewer. It is correct that our optimization of magnetic system is based on maximize the cooling capacity. The synchronization of heat transfer fluid with two-fold symmetry of magnetization in the rotary refrigeration. For simplicity of rotary refrigeration, we still keep the two-fold symmetry in each heating and cooling cycle. In the future, a complex rotary refrigerator cooling system adapting the asymmetry cycle in synchronizing the magnetic duty cycle can be scrutinized, in which the cooling circulating system will be of more complex in design.

 

3. Do the authors of the article consider the variation of the rotor speed, which can be achieved using a stepper motor? This variation can significantly affect the duty cycle.

Reply: Thanks the suggestion of the reviewer. We also change the rotor speed with 1 s, 2 s and 4 s cycle time. The difference is the time to reach the thermal equilibrium after several hundred cycles at the situation of the cooling water cycle already synchronized with the magnetic rotor. The optimized magnetic duty cycle is not changed. 

 

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors of the article responded to the comments in great detail and expanded the description of the simulation procedure. Therefore, this article can be accepted for publication in its present form.