Prediction of Critical Heat Flux for Subcooled Flow Boiling in Annulus and Transient Surface Temperature Change at CHF

Round 1

Reviewer 1 Report

The manuscript describes, for a vertical annulus, the procedure to predict the critical heat flux and the wall temperature of the heater, which is placed as the inner rod of the geometry. The results provided by the model were compared with the experimental results available in the open literature.

Even though, form a physical pint of view, the topic is interesting the analysis of the open literature shows that its relevance is not significant. Among the references of the manuscript the newest is 9 years old (2013), moreover the largest part (15 references over 21) is earlier than year 2000. In the end, an overview of the literature reveals that no works on the topic were done in the last 5 years. So, the authors, at least in the introduction, should provide examples of possible application involving annuli and the risk of dry out and explain why the topis is important today.

The manuscript has several issues that requires to be fixed before publication.

• The nomenclature is missing.
• The references are obsolete.
• As the procedure is based on empirical correlations too, the authors should report the uncertainty related to the predictions.
• The uncertainty of the experimental date used to benchmark the procedure should be reported.
• The format and the explanation of the tables and the figures should be improved (e.g. Does figure 6 refer to space or time? Which is the positive direction of the axis?
• The explanation of the model should be improved. For instance, in section 4.2 a better description is required, the manuscript suggests that a periodic behavior is taken into account: subcooled liquid at the wall, dryout, nucleate boiling, subcooled liquid again… which is the meaning of the initial condition? Which is the temperature distribution in the heater reported in equation (17)? According to what it is possible to state that the heat transfer coefficient in the vapor stream is h=100Wm^-2K^-1, it is not explained how the integration of equation 15 was performed.
• A general review of the symbols, units, and the reference to the equations is required (e.g. in table 3 the thermal conductivity is indicated with lambda instead of k, at line 171 the equation reference should be 17 instead of 10, for equation 18 it should be reported the units to be used for P).
• As the procedure aims to predict the critical heat flux and the wall temperature a comparison with experimental data should be provided also for the latter quantity (or at least explain why it is not done).

Author Response

The manuscript describes, for a vertical annulus, the procedure to predict the critical heat flux and the wall temperature of the heater, which is placed as the inner rod of the geometry. The results provided by the model were compared with the experimental results available in the open literature.

Even though, form a physical pint of view, the topic is interesting the analysis of the open literature shows that its relevance is not significant. Among the references of the manuscript the newest is 9 years old (2013), moreover the largest part (15 references over 21) is earlier than year 2000. In the end, an overview of the literature reveals that no works on the topic were done in the last 5 years. So, the authors, at least in the introduction, should provide examples of possible application involving annuli and the risk of dry out and explain why the topis is important today.

Answer:

Thank you very much for your comments. As you suggested, we included more references in the revised paper.

CHF prediction from mechanistic models is an important issue for high heat flux components. The research is on the way and is far from solved. This paper deals with CHF in an annulus, which is the most basic flow geometry simplified from a fuel bundle in a reactor core. Our research is a unique and new approach to CHF prediction. This is the reason that there are not too many references in recent years. However, it doesn’t mean that our topic is not important.

The manuscript has several issues that require to be fixed before publication.

• The nomenclature is missing.

Answer: Thank you very much for your comments. The nomenclature is included.

• The references are obsolete.

Answer: Thank you very much for your comments. We included more references.

• As the procedure is based on empirical correlations too, the authors should report the uncertainty related to the predictions.

Answer: Thank you very much for your comments. The model itself has no empirical constants. As to the liquid viscosity profile that is needed in the calculation, we used the Norii correlation. Besides the liquid viscosity profile, we also used the empirical correlations for NVG point, friction factor, quality, void fraction, and drag coefficient on the bubble… Actually, it is impossible to report all the uncertainties related to all these predictions. We only compare the predicted CHF with experimental CHF.   So far, lots of mechanistic models have been proposed and all of them inevitably employed the empirical correlations as well, and none of them ever discussed the uncertainties related to the correlations.

• The uncertainty of the experimental data used to benchmark the procedure should be reported.

Answer: Thank you very much for your comments. The uncertainty of the experimental data used to benchmark was reported in the original papers. It is not the content of this paper.

• The format and the explanation of the tables and the figures should be improved (e.g. Does figure 6 refer to space or time? Which is the positive direction of the axis?

Answer: Thank you very much for your comments. The original fig.6 was a little difficult to understand. We revised the fig.6 and hope the new figure is easy to understand.

• The explanation of the model should be improved. For instance, in section 4.2 a better description is required, the manuscript suggests that a periodic behavior is taken into account: subcooled liquid at the wall, dry out, nucleate boiling, subcooled liquid again… which is the meaning of the initial condition? Which is the temperature distribution in the heater reported in equation (17)? According to what it is possible to state that the heat transfer coefficient in the vapor stream is h=100Wm^-2K^-1, it is not explained how the integration of equation 15 was performed.

Answer: Thank you very much for your comments. We made big revisions to section 4.

The initial condition for a CHF in subcooled flow boiling is a nucleate boiling condition, which gives a surface temperature calculated from Jens - Lottes correlation (equation (18) in old paper, equation (19) in revised paper). The initial condition (equation (17)) is derived by solving the thermal conduction equation (15) by using Jens - Lottes correlation for the surface temperature.

We solved the thermal conduction equation written for the heater in cylindrical coordinate. From which the temperature distribution in the heater was derived. But in the paper, we didn’t report the temperature distribution inside the heater but only report the surface temperature of the heater. This is because, in CHF experiments, only the surface temperature is generally measured and reported.

In the paper, the heat transfer coefficient in the vapor stream is set to h=100Wm^-2K^-1. this is the order of the heat transfer rate evaluated from correlation for convective heat transfer in vapor.

• A general review of the symbols, units, and the reference to the equations is required (e.g. in table 3 the thermal conductivity is indicated with lambda instead of k, at line 171 the equation reference should be 17 instead of 10, for equation 18 it should be reported the units to be used for P).

Answer: Thank you very much for your comments. We revised the paper based on your comments.

• As the procedure aims to predict the critical heat flux and the wall temperature comparison with experimental data should be provided also for the latter quantity (or at least explain why it is not done).

Answer: Thank you very much for your comments. We want to compare the calculated wall temperature with the experimental one, but there is no such detailed experimental wall temperature data at CHF has ever been reported in literature.

Reviewer 2 Report

1) For the calculation of the  liquid phase velocity distribution, the model of karman has been exposed in a sufficiently detailed way and with explanatory figures, while that of Nouri used in this work is almost parachuted. I recommend justifying the choice of the Nouri correlation and adding explanatory figures for the case of a ring as it was done for Karman. If it is a similar representation of the figure, then I prefer to reserve the figure illustration for Nouri instead of Karman.

2) Discuss in a qualitative way the value of 20% regarding the prediction of the CHF: Importance of the difference? its impact? ... By the way, for the 20% I ask you to see the comment 5)

3) Which chapter 2 are you talking about in line 206 of the article?

4) In line 203 of the article: another calculation table must be presented for Mass flux = 512kg/m2s

5) According to a small calculation of figure 5, the value that I found is 30% and not 20%! Indeed: [250(experimental value) - 175 (calculated value)]/250 = 30%!

Author Response

1) For the calculation of the liquid phase velocity distribution, the model of Karman has been exposed in a sufficiently detailed way and with explanatory figures, while that of Nouri used in this work is almost parachuted. I recommend justifying the choice of the Nouri correlation and adding explanatory figures for the case of a ring as it was done for Karman. If it is a similar representation of the figure, then I prefer to reserve the figure illustration for Nouri instead of Karman.

Answer: Thank you very much for your comments. Karman model is for a circular and Nouri correlation is for an annular. Their objects are different and can’t be used to each other. In the initial process of the CHF prediction, we didn’t realize the difference of liquid velocity profiles between a circular tube and an annulus, and we used the Karman model to calculate the liquid velocity profile. However, the prediction result was not good at all. It took us a quite long time to realize that we used the wrong model for the liquid velocity profile.

2) Discuss in a qualitative way the value of 20% regarding the prediction of the CHF: Importance of the difference? its impact? ... By the way, for the 20% I ask you to see the comment 5)

Answer: Thank you very much for your comments. The lower the difference shows a better prediction, which is near to the experimental one.

3) Which chapter 2 are you talking about in line 206 of the article?

Answer: Thank you very much for your comments. Chapter 2 is section 2 of the paper.　We revised the paper.

4) In line 203 of the article: another calculation table must be presented for Mass flux = 512kg/m2s

Answer: Thank you very much for your comments. From section 3, we know that our model predicts CHF better at high mass flux than low mass flux (high mass flux is a more subcooled boiling condition). That is why we choose the Mass flux =1239 kg/m2s as the analysis case in section 4. Although we can report the detailed information for Mass flux = 512kg/m2s condition, because it is not our analysis case, we don’t see the necessity to report it.

5) According to a small calculation of figure 5, the value that I found is 30% and not 20%! Indeed: [250(experimental value) - 175 (calculated value)]/250 = 30%!

Answer: Thank you very much for your comments. we revised 20% to 30% as you suggested, including Fig.5.

Round 2

Reviewer 1 Report

The manuscript describes, for a vertical annulus, the procedure to predict the critical heat flux and the wall temperature of the heater, which is placed as the inner rod of the geometry. The results provided by the model were compared with the experimental results available in the open literature.

Changes to the manuscript were done, but issues remain and some remarks, highlighted in the previous review, were not properly replayed.

The authors added the nomenclature (which makes easier the understanding of the equations) but it is incomplete, for instance, the surface tension “sigma” and the Reynolds number (?) “Re” are missing.

The general frame of the manuscript should be improved because of the issues listed below.

[+] In the text there are useless parts.

E.g. in section 2, the velocity distribution for single phase flow inside an annulus is reported in equation 11, which makes equation 10 unnecessary.

[+] Important parts are missing.

In equation 12 is not provided the expression for the Reynolds number (?) Re, to be used in equation 12, is not reported. Moreover, the authors did not mention the boundary conditions related to the experimental data used to benchmark the model. Did the experiments were performed fixing the surface temperature or the heat flux or something else?

The authors did not report the validity range of their model, as it relies on empirical correlations it cannot be used for any operating conditions.

According to figure 6 at different axial positions there are different heat transfer mechanisms, that makes the heat transfer coefficient a function of the axial position and the same hold also for the temperature. Nevertheless, in equation 16 the axial coordinate is not considered. The authors should provide an explanation.

The whole initial temperature distribution in the heating element should be provided, the temperature in a single point (the surface) is not enough. The initial temperature distribution is required to solve the equation 16 “thermal conduction equation”, not the opposite!

According to what it is possible to state that the heat transfer coefficient in the vapor stream is h=100Wm^-2K^-1, a correlation or a reference should be provided.

In equation 17 is unclear what Tf represents. According to the definition of the h provided in equation 21 it should be the liquid-vapor interface temperature, but a model for such a temperature is not reported.

[+] There are unclear parts.

E.g. according to equation 20 the liquid single-phase heat flux seems independent of the fluid temperature while the heat flux transferred by boiling is a function of the total heat flux. If they are replaced inside the first equation the equality could not be true.

[+] Mistakes are present.

In equation 11 the condition related to the third equation has to be fixed.

The statement at line 230÷232 is wrong. The volumetric heating rate and the critical heat flux are different quantities (their units are different too) and it is not possible to compute the former multiplying the latter by a constant. That makes, at least, the following part of the paper meaningless.

Author Response

Thank you very much for your hard work on my paper review. I replied to your question and comments in the attached file. The paper was revised a lot based on your precious comments.

Author Response File: Author Response.docx

Reviewer 2 Report

I accept in present form.

Author Response

Thank you very much for your kind review.