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Peer-Review Record

Mathematical Models for Simulation and Optimization of High-Flux Solar Furnaces

Math. Comput. Appl. 2019, 24(2), 65; https://doi.org/10.3390/mca24020065
Reviewer 1: Chuang Sun
Reviewer 2: Anonymous
Math. Comput. Appl. 2019, 24(2), 65; https://doi.org/10.3390/mca24020065
Received: 10 May 2019 / Revised: 7 June 2019 / Accepted: 17 June 2019 / Published: 21 June 2019

Round 1

Reviewer 1 Report

Mathematical Models for Simulation and Optimization of High-Flux Solar Furnaces

In this manuscript, the ray-tracing method is used to simulate the three different model, and the author hope the results is helpful for the solar furnace SF60. the topic of the manuscript is important and interesting, while the new idea about the manuscript is not presented. Moreover, the manuscript is not well written, like the introduction. Therefore, the reviewer think the present state of the manuscript is not available for MCA and must be major modified.

(1) The Introduction part containing a lot of background statements is too long, and the author only used the review article (literature [12]) to summarize the state-of-the art about the sunrays simulating, it is far from enough. Nowadays, the development and application of solar energy is a research focus, and the ray simulation and analysis is one of the key points, therefore, there should be a lot literature about this research, and the author should rewrite the introduction.

(2) As the author said, the ray-tracing method is a complete simulation method and there are so many software about it. In order to exactly satisfy the author needs, the corresponding code is built by the author. The reliability and accuracy need to be explained in the manuscript. On the other hand, the three design modes in the manuscript is not complicated, therefore, the reviewer wonders to know the new idea about this manuscript.

(3) The format of the manuscript is not standard. Equations should not be given as a figure and the figure captions are too long, the related explanations for the figure should be in the next text.

(4) The title of the manuscript is “Mathematical Models for Simulation and Optimization of High-Flux Solar Furnaces”. Which parts of the manuscript is about the optimization.

Author Response

We thank Reviewer 1 for the comments which allowed us to improve and change considerably the manuscript. Please see point-by-point our responses to the comments:

 

Point 1: The Introduction part containing a lot of background statements is too long, and the author only used the review article (literature [12]) to summarize the state-of-the art about the sunrays simulating, it is far from enough. Nowadays, the development and application of solar energy is a research focus, and the ray simulation and analysis is one of the key points, therefore, there should be a lot literature about this research, and the author should rewrite the introduction.

 

Response 1: Following the reviewer’s comment, the Introduction was shortened. Compared to the initial version with circa 900 words, the present text of the Introduction contains 800 words.

Concerning the subsequent part of the comment, please note that the review article [12] (Fernández-González et al. Concentrated solar energy applications in materials science and metallurgy. Solar Energy 2018, 170, 520–540) was not mentioned to summarize the state-of-the art about the sunrays simulations. Literature review about ray simulation is done in section 2. Ray tracing simulation (references no.16 till no.35).

 

Point 2: As the author said, the ray-tracing method is a complete simulation method and there are so many software about it. In order to exactly satisfy the author needs, the corresponding code is built by the author. The reliability and accuracy need to be explained in the manuscript. On the other hand, the three design modes in the manuscript is not complicated, therefore, the reviewer wonders to know the new idea about this manuscript.

 

Response 2: It is the first time that ray-tracing simulations of a solar furnace like SF60 are presented in the literature accompanied by the theoretical equations that are used. Additionally, we have introduced two other topics in the revised version, and for that ‒ just before section 4. Conclusions and prospects for future work ‒ the following text was introduced (together with two new figures):

(1)   As another example, Figure 18 compares experimental data obtained with a radiometer (Vatell Thermogage 1000-4, with a sensitivity = 2mV per W/cm2), with a circular measurement area (diameter = 5/8 in = 15.9 mm), with data calculated using our software. The results obtained for the flux of energy (in kW/m2), 475 mm and 730 mm below the 45° mirror, for the SF60 solar furnace, are quite satisfactory, given the natural limitations of the experimental infrastructure.

(2)   Finally, we show how this software can contribute to develop new devices, such as the flux concentrator shown in Figure 19, with a geometry similar to SF60 (a focal distance of 7450 mm and a rim angle of 38°). The parallel rays (1) coming from the sun are reflected in the large, concave, paraboloid, before being concentrated (2 and 3) to the focal point F. If these rays are reflected by a small paraboloid with the same focal point of the big one ‒ convex such as paraboloid A or concave such as paraboloid B ‒ then our calculations show that the reflected rays (4 and 5) are simultaneously highly concentrated and equally distributed over the narrow illuminated region (with a very small hole in the middle, due to the shadow produced by the second paraboloid, probably too small to be detectable). For this example, we arbitrarily chose 250 mm for the projected radius of the small paraboloid, which seems adequate for the dimensions of SF60. If proven experimentally valid, this design circumvents one of the major issues with high flux concentrators: the Gaussian distribution usually predicted for the radial flux of energy, making it difficult to obtain a homogeneous source of concentrated energy with these solar furnaces.

 

Point 3: The format of the manuscript is not standard. Equations should not be given as a figure and the figure captions are too long, the related explanations for the figure should be in the next text.

 

Response 3: Following the reviewer’s comment, equations have been taken out of the figures. Some of the figure captions have been shortened.

 

Point 4: The title of the manuscript is “Mathematical Models for Simulation and Optimization of High-Flux Solar Furnaces”. Which parts of the manuscript is about the optimization.

 

Response 4: Our ultimate goal to pursue the simulations is always the optimization of the solar furnace layout, namely the experimental setup. In this paper, we discuss several examples of optimization: (1) the position of the 45° tilted mirror; (2) the influence of the attenuation shutters on the energy flux profile reaching the testing table; (3) a new layout using two paraboloids to attain homogenous distribution of energy flux (a very important issue for solar furnaces).

 

NOTE: Due to the extensive changes introduced (because equations have been taken out of the previous figures), only new text is shown in red colour in the new version.


Reviewer 2 Report

This paper needs the following major revisions and then reconsideration for possible publication:

A) Please remove the equations from the figures. Give the equations inside the text with numbering and references where it is possible. The figures have to be only schemes and no equations.

B) Please use any metrics for the intensity and the variation of the heat flux. Maybe the deviation and the mean value in every case.

C) I think that the results can be expressed in terms of power (Watt) and parameters such as the optical efficiency to be given.

D) Use numerical results in the abstract and the conclusions.


Author Response

We would like to thank for the comments which we received from Reviewer 2. Please see our responses:

 

Point 1: Please remove the equations from the figures. Give the equations inside the text with numbering and references where it is possible. The figures have to be only schemes and no equations.

 

Response 1: Following the reviewer’s comment, equations were removed from the figures. This action causes a complete different arrangement compared to the previous version.

 

Point 2: Please use any metrics for the intensity and the variation of the heat flux. Maybe the deviation and the mean value in every case.

 

Response 2: Throughout this work we assume that the number of rays reaching a given point is directly proportional to the flux of energy, measured in kW/m2. During the recent years we accumulated an extensive amount of experimental data (that we intend to publish elsewhere) that confirms this assumption. To provide a better insight into the comparison of our calculations with experimental date, we introduced (as an example) a new figure showing experimental and calculated data for the flux of energy (in kW/m2): see Figure 18. The following text was added:

As another example, Figure 18 compares experimental data obtained with a radiometer (Vatell Thermogage 1000-4, with a sensitivity = 2mV per W/cm2), with a circular measurement area (diameter = 5/8 in = 15.9 mm), with data calculated using our software. The results obtained for the flux of energy (in kW/m2), 475 mm and 730 mm below the 45° mirror, for the SF60 solar furnace, are quite satisfactory, given the natural limitations of the experimental infrastructure.

 

Point 3: I think that the results can be expressed in terms of power (Watt) and parameters such as the optical efficiency to be given.

 

Response 3: See Response 2. Results obtained by this type of ray-tracing simulations are always in arbitrary units (as a number of counts, like for example a X-ray detector). Afterwards, it is always needed some sort of calibration in order to compare with experimental measurements.

 

Point 4: Use numerical results in the abstract and the conclusions.

 

Response 4: Please note that, according to the Instrutions for authors in the MCA template, there is a restriction of maximum 200 words for the Abstract. However, at the beginning of section 4. Conclusions and prospects for future work we added the following text:

The 109 rays used in our simulations proved enough to give an accurate description of the light behaviour which can be adequately compared to the experimental flux of energy in kW/m2.



NOTE: Due to the extensive changes introduced (because all equations were removed from the previous figures), only new text is shown in red colour in the new version.



Round 2

Reviewer 1 Report

The authors addressed the reviewer's questions well, and modified the manuscript.

Reviewer 2 Report

The paper ha sbeen properly revised.

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