Review Reports - Investigation of Turbulence and Turbulent Prandtl Number Models for He-Xe Thermal Hydraulics in Quasi-Triangular Channel

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The present work is definetely of interest for the readers of the journal and presents a meaningful scientific contribution. However, I have several comments that will improve the final version of the Ms:

When refering to condition 1, it is not clear what are the parameters, please explicitly state these parameters.
It is not clear what is the flow regime at the inlet. Is it laminar or turbulent? I suppose it is turbulent due to the study. Is it imposed? Again, what are the parameters? In the study just the Pr number is assumed and the thicknesses among flow and thermal boundary, are there any other ssumptions?
A discussion regarding the appplicability of the best-performing models is needed, could they be valid for different flow conditions?
In Figure 4 please indicate that these are wall temperature result at the mid-concave region of the 247 quasi-triangular channel.
In Figures 7, 9, 10 and 11 indicate that these are radial turbulent Pr profiles taken along the concave-to-narrowest-section midline of the quasi-triangular channel. Indicate the direction of the radial coordinate and the flow regime in each plot.
In all figures if symbols are used, please explain them in the caption.
If needed please include if the profiles correspond to the top, middle or bottom region in the figures.
Include data source from experimental curves (reference).
Finally please state explicitly the novelty of your work, it needs to be in the introduction, abstract and conclusions. State that this is the first systematic evaluation of both turbulence Pr models for He-Xe in quasi triangular channels with experimental validation.

Comments on the Quality of English Language

Spelling and finger errors such as: diffenent, futher, Taylars, het, among others.
Long phrases in Results and Discussion sections should be changed to shorter and clearer statements.
Verify consistent use of notation and symbols.
Use past tense for actions performed and present tense for statements.
Proofread captions and in text figure references.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The article is clearly written and well-structured. With a few minor revisions, it is suitable for publication in Energies. Detailed comments and suggestions are provided below.

1. In section 2.1, as the authors stated “(RANS) equations under steady-state conditions” so Eqs. (1)-(3) should read in steady-state conditions. In addition, revise Eq. (2) since it is not fully corrected.

2. As the authors stated, “The original channel consists of three components: unheated round tube sections at the inlet and outlet, and a quasi-triangular tube section in the middle.”. In this way insert a figure with the dimension of each component.

3. The reason for generating a mesh on the tube wall is unclear, given that it is not included in the modeling.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This research paper examines theoretical models of flow dynamics and turbulence development in helium-xenon mixtures. Using the turbulent Prandtl number model, the authors attempt to theoretically predict the temperature distribution of this kind of mixture within tight-lattice rod bundle channels. The channels, designed for compact cooling systems in nuclear reactors, feature tubes with quasi-triangular cross sections instead of traditional circular ones.

The introduction of the text lacks sufficient background information and does not include all relevant references. It is not clearly explained why the authors consider the He-Xe mixture to be optimal for the present study. Furthermore, the manuscript does not specify the type of material used to construct the cooler that contains the He-Xe mixture, nor does it clarify the material requirements that could enhance the thermal conductivity and reduce the viscosity of this mixture.

The research design does not appear to be appropriate. The text lacks a clear justification for including previously published numerical simulations on heat transfer in He-Xe gas mixtures. The authors do not adequately explain why these earlier models are presented or critically assess their advantages or critically assess their advantages or limitations, especially considering that most of these models yield results similar to those shown in Figure 4 of the current manuscript. Furthermore, the rationale for presenting wall temperature data under different grid resolutions (Figure 3) is unclear, particularly if the results are grid independent.

The presentation of the research results appears to be inadequate. For example, Table 5, which presents the wall temperature prediction error for different turbulence models, and Table 6, which shows the prediction error across different regions, lack enough context to be meaningful. Presenting prediction errors without the corresponding actual temperature values diminishes the physical relevance of the data. In their current form, these tables offer limited insight, as errors are detached from the underlying physical quantities that they aim to evaluate.

The research paper does not appear to be particularly original, but it is scientifically sound and, with a revision, could be of interest to readers. The scientific value of the manuscript could be improved by providing a clearer explanation of what is meant by the ‘optimal performance’ of the He-Xe mixture and the design of the nuclear reactor itself, as mentioned in line 20 of the manuscript. Defining this concept more precisely would help the reader better understand the objectives and significance of the study.

The conclusion section lacks clarity and focus. The statement that one model proposed by other authors is more consistent with another model, also proposed by other authors, is not appropriate for the conclusions. This section should emphasize the significance and potential of the results obtained by the authors themselves, clearly explaining their meaning and possible applications. Furthermore, the manuscript does not adequately justify why the subject of this research is suitable for publication in the journal Energies.

The general merit of the paper is low. However, with some shortening and thorough revision, its quality and impact could be significantly improved. Additionally, there are several technical remarks regarding the manuscript text, as outlined below:

The introduction lacks a discussion or demonstration of results comparing the He-Xe mixture with other possible noble gas mixtures. What are the arguments supporting the claim that He-Xe is the most suitable coolant for noble gas-cooled reactors?
The Prandtl number acronym is inconsistently formatted throughout the manuscript, in italic format is given in some instances, and in regular font in others. This formatting should be uniformed for clarity. In particular, when the acronym appears in equations, such inconsistencies may lead to confusion as to whether it represents the same parameter or a different one (see, e.g., lines 44, 89, 95, 107, etc.).
The author's name should be presented in uppercase letters (see line 95). Additionally, there is inconsistency in the referencing style throughout the manuscript. In some cases, references are given in square brackets in numerical format, while in others, the author’s name is used within the brackets. This formatting should be uniform and given in accordance with the journal's citation guidelines.
A space is missing between the word and the citation in line 96. This should be corrected to maintain proper formatting and readability.
Mistyping error: ‘medol’ should be corrected in ‘model’ on line 108.
In the ‘Reynolds Time Average Equation (RANS)’ the acronym RANS does not accurately reflect the capitalized initials of the terms used.
Equations (1) to (4) exhibit inconsistencies in the formatting of the parameters u_i, u_j, which appear in both italic and regular fonts. This inconsistency may suggest that they represent different quantities. If they denote the same physical parameter, the formatting should be unified throughout. If they are meant to be distinct, this distinction must be explicitly clarified in the text. A similar issue occurs in the body of the text where these parameters are mentioned (see line 121). Additionally, the meaning of the overbars (top dashes) in equations (2) to (5) should be clearly explained, as their significance is not currently defined.
When a sentence ends with an equation, the equation should be followed by a period. If the equation appears in the middle of a sentence, it should be followed by a comma, see equations (1) to (14).
Figures 3, 4, 6 and 8 are not very informative. They appear too similar and give the impression of repetition. A similar issue applies to Figures 7, 9, 10 and 11, which also lack clarity in presentation and distinct value. It is recommended to consider merging these figures where appropriate and discussing some of the less significant results directly in the text instead. Furthermore, Figures 1 and 2 seem to have the potential to be effectively combined into a single figure.

Comments on the Quality of English Language

The English could be improved to more clearly express the research.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for carefully incorporating the suggested comments into your revised version of the manuscript. The paper is now clearer and more accessible to readers. However, there are still a few points that could be further improved to enhance the overall quality of the presentation:

A brief explanation is lacking as to why He–Xe mixtures are used as coolants in compact nuclear reactor systems.
IntroductionThis section should be expanded with additional explanations to provide a stronger context and background.

In line 42, the statement “… enable substantial reductions in system volume and mass …” would benefit from quantification. Indicate the approximate rate or extent of these reductions;
On line 45, the statement “… constitute a good solution …” could be strengthened by briefly explaining why this solution is considered good;
At line 47, the phrase “… significant advantages …”should be followed by a short description of what these advantages are;
In line 49, the statement “… critical for thermal-hydraulic safety …” should be elaborated by briefly explaining why this aspect is critical;
On line 50, the phrase “…low Prandtl number…” requires clarification. Please specify the reason for this low value, since the Prandtl number can be influenced by a low specific heat capacity, low dynamic viscosity, or high thermal conductivity. This information is currently missing from the Introduction and would be valuable for readers.
In line 51, the comparison. The phrase “… pressurized water used in light water reactors …" has a higher value of Prandtl number would be clearer if you provided the approximate numerical value or at least the rate of difference.

In Equation (12), the curly braces should be formatted using the “Equation” tool from the pull-down menu rather than inserted as regular text symbols.
In Equation (14), the symbol Pr_t,loc is presented with the subscript in italics, whereas in line 376 the same symbol appears in normal style. For consistency, the notation should be uniform throughout the manuscript.
It is not necessary to present Figures 6, 8, 9, and 10 separately, as they are very similar. They can be combined into a single figure (e.g., Figure 6), with sublabels (6a, 6b, 6c, 6d). This arrangement would make it much easier for readers to compare the results by viewing the complete picture at once.

The Conclusions section should more explicitly specify and, if possible, quantify the advantages of the proposed calculation method. In particular, it would be helpful to indicate the extent to which this approach improves understanding of processes in compact nuclear reactor systems or enhances the exploitation of coolants in such systems. Also, clarify what practical problems can be addressed or what improvements could potentially be introduced in reactor operation based on the results of these calculations.