Analysis of Unsteady Heat Transfer in the Pre-Cooling Process of 300 m3 Liquid Hydrogen Tank
Round 1
Reviewer 1 Report
Manuscript Number: Processes-2230817
Title: Analysis of Unsteady Heat Transfer in the Pre-cooling Process of 300 m3 Liquid Hydrogen Tank
Decision: Minor revision
Article Type: Article
The article is, in general, well written but there are some issues that article should consider to revise in order to improve its quality. Some comments were done in this way:
Ø More emphasis should be placed on the importance of study at the end of the Introduction.
Ø Fig. 4 image quality is poor.
After making the above corrections would recommend this article for publication in Processes.
Author Response
Comment 1：More emphasis should be placed on the importance of study at the end of the Introduction.
Responses: The manuscript has been changed as required: “Currently, the pre-cooling process parameters of liquid hydrogen tanks are primarily obtained through engineering tests. A theoretical calculation model is needed for sys-tematic research, which makes the establishment of corresponding standards for the pre-cooling of liquid hydrogen tanks lack a theoretical basis.”
Comment 2：Fig. 4 image quality is poor.
Responses: Figure 4 has been replaced as required.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The authors presented a study of the Unsteady Heat Transfer in the Pre-cooling Process of 300 m3 Liquid Hydrogen Tank
The introduction is very short and should be extended.
The novelty of the paper is to be clearly stated.
A figure presenting the studied configuration is to be added.
The assumptions used in the establishment of the equations are to be justified.
The iterative calculation is to be described with more detail.
What is the convergence criterion?
Figure 2 is not cited in the text.
The result presented in Fig 4 is very confusing: why have you used Fluent? Why not all the process is studied using Fluent? The boundary conditions and the equations solved to get this result are to be presented and described
Fig 4 shows that there is not any vertical variation of the temperature. So it can be considered as 1D variation.
What do you mean by static temperature in the legend of Fig 4?
What is the interest of presenting Table 2?
The discussion is to be improved by physical interpretations.
The paper is to be checked against misprints and grammatical mistakes.
Author Response
Comment 1：The introduction is very short and should be extended.
Responses: The manuscript has been changed as required: “Currently, the pre-cooling process parameters of liquid hydrogen tanks are primarily obtained through engineering tests. A theoretical calculation model is needed for systematic research, which makes the establishment of corresponding standards for the pre-cooling of liquid hydrogen tanks lack a theoretical basis.”
Comment 2：The novelty of the paper is to be clearly stated.
Responses: The manuscript has been changed as required: “Currently, the pre-cooling process parameters of liquid hydrogen tanks are primarily obtained through engineering tests. A theoretical calculation model is needed for systematic research, which makes the establishment of corresponding standards for the pre-cooling of liquid hydrogen tanks lack a theoretical basis. Based on the mass and energy balance principle under certain assumptions, an innovative pre-cooling model has been established for 300 m3 liquid hydrogen tanks to calculate the dynamic change trends of inner temperature and cold source mass consumption at different cooling rates. The pre-cooling process parameters under different working conditions have been compared and analyzed. The results provide theoretical support for selecting practical pre-cooling process parameters of cryogenic propellant tanks.”
Comment 3：A figure presenting the studied configuration is to be added.
Responses: Figure 1 is added as required, which shows the structure of liquid hydrogen storage tank and heat during precooling.
Comment 4：The iterative calculation is to be described with more detail.
Responses: More details about the iterative calculation have been added. “The practical pre-cooling process is unsteady and is regarded as a steady process per unit of time in programming calculation to simplify the analysis. The temperature variation dTn within every unit of time was calculated with equations (4) - (8), and hydrogen temperature Tn could be obtained. Within the first unit time, Q1- Q4 could be calculated with equations (2) and (9) - (12), then the pre-cooling medium mass consumed was obtained with equations (1) and (13). From the second unit time to the end of the calculation, the calculation process of each unit time is the same as that of the first unit time. The pre-cooling medium mass within every unit of time obtained. The total pre-cooling mass is obtained by adding the consumed mass of each unit of time with equation (14). Finally, various heat weights are calculated with equations (15) - (16). Accordingly, the pre-cooling process's iterative calculation was done until the in-ner temperature reached the boiling temperature of the propellant. The pre-cooling process was programmed with MATLAB software in the paper. Figure 2 shows the flow diagram of the pre-cooling parameter calculation.”.
Comment 5：What is the convergence criterion?
Responses: The convergence criterion is described in Page 5. “Accordingly, the pre-cooling process's iterative calculation was done until the inner temperature reached the boiling temperature of the propellant.”
Comments 6：Figure 2 is not cited in the text.
Responses: Figure 3 is cited in the text: “Figure 3 shows the fitted specific heat of liquid and solid materials in a liquid hydrogen tank.”
Comments 7：The result presented in Fig 4 is very confusing: why have you used Fluent? Why not all the process is studied using Fluent? The boundary conditions and the equations solved to get this result are to be presented and described
Responses: The purpose of the Section 3.3 is to calculate the temperature distribution and average temperature of the insulation layer at the end of precooling, and then obtain the liquid hydrogen mass required for cooling the insulation layer. Using fluent to calculate the temperature distribution from the inner wall to the outer wall is very simple and the workload is less. If fluent is used to calculate the whole precooling process, the grids number is particularly large due to the huge size of the 300m3 liquid hydrogen storage tank and phase change of the liquid hydrogen. At the same time, there are many research cases in this paper, so a large amount of calculation is needed and the analysis is relatively complex, which is not suitable for the engineering applications. So, this paper does not use fluent to study all processes. The boundary conditions and the models selected in the FLUENT solved to obtain the results are described as required.
“A heat transfer analysis model was established to obtain the temperature distribution of the interlayer materials at the end of the pre-cooling process, considering the heat conduction and radiation from the inner wall to the external wall. The diameter of the inner tank was 4,200 mm, the wall thickness was 14mm, and the internal wall temperature was 20.4K. The diameter of the external tank was 4,800 mm, the wall thickness was 14mm, and the exterior wall temperature was 293.15K. The thickness of the multi-layered thermal insulation materials was 60 mm. The apparent thermal conductivity was 2x10-5W/(m•K), and the emissivity of the double-faced aluminized film was 0.05. The radiation model is selected as “surface to surface.” The temperature distribution was obtained after calculation with the FLUENT software and is shown in Figure 5.”
Comment 8：Fig 4 shows that there is not any vertical variation of the temperature. So, it can be considered as 1D variation.
Responses: The purpose of the Section 3.3 is to calculate the temperature distribution and average temperature of the insulation layer at the end of precooling, and then obtain the liquid hydrogen mass required for cooling the insulation layer. In order to simplify the calculation process, only the solid heat conduction and radiation from inside wall to outside wall are considered, so the temperature change is one-dimensional. The corresponding expression has been changed as follows:
“A heat transfer analysis model was established to obtain the temperature distribution of the interlayer materials at the end of the pre-cooling process, considering the heat conduction and radiation from the inner wall to the external wall. The diameter of the inner tank was 4,200 mm, the wall thickness was 14mm, and the internal wall temperature was 20.4K. The diameter of the external tank was 4,800 mm, the wall thickness was 14mm, and the exterior wall temperature was 293.15K. The thickness of the multi-layered thermal insulation materials was 60 mm. The apparent thermal conductivity was 2x10-5W/(m•K), and the emissivity of the double-faced aluminized film was 0.05. The radiation model is selected as “surface to surface.” The temperature distribution was obtained after calculation with the FLUENT software and is shown in Figure 5.”
Comment 9：What do you mean by static temperature in the legend of Fig 4?
Responses: The static temperature in the legend in Figure 4 is the actual temperature of the actual tank wall material and thermal insulation material, which is relative to the total temperature in the FLUENT graphic display.
Comment 10：What is the interest of presenting Table 2?
Responses: Table 2 lists pre-cooling time, total mass of liquid hydrogen consumed, proportions of various heat loads and total liquid hydrogen flow at different cooling rates. All the data in Table 2 shows a comprehensive comparison of the parameters of various precooling conditions.
Comment 11：The discussion is to be improved by physical interpretations.
Responses: The discussion is to be improved as required. Physical interpretations have been added into Section 4.1. “Generally, q1 - q3 went up and then down with the fall of temperature in the pre-cooling process, as they had a positive correlation with the specific heat of materials and temperature change rate per unit of time, which played a dominant role. Figure 4 shows that the temperature change rates went up and down to keep corresponding temperature change trends. In the pre-cooling process, q4 kept rising, negatively correlated with the temperature, and was non-relevant to temperature change rates. When q1 is the maximum, the corresponding temperature is 27 K, that of q2 was 106 K, and that of q3 was 134 K. In different pre-cooling stages, the proportion of liquid hydrogen consumed by the four heat loads is different. q4 had the most significant proportion ranging from 85% to 95% at the beginning and end of pre-cooling. The reason is that pre-cooling needs to offset the external heat initially, and all materials have been pre-cooled at the end. In the middle pre-cooling process, q1 and q2 accounted for a more significant proportion with the maximum values of 60% and 90%, respectively, because the steel’s mass and the hydrogen’s specific heat are relatively large. The maximum proportion of q3 is 6%, which does not play a leading role in the pre-cooling process.”
Comment 12：The paper is to be checked against misprints and grammatical mistakes.
Responses: The paper has completed the correction of printing errors and grammatical mistakes.
Author Response File: Author Response.docx
Reviewer 3 Report
The mathematical model for the pre-cooling process of cryogenic propellant tanks was proposed and used for the analysis of the pre-cooling process of a 300 m3 liquid hydrogen tank.
The experimental model is not described very well. The part describing the mathematical model needs to be improved. The presented model is very simplified. Some factors affecting heat transfer during liquid boiling and evaporation are not discussed and taken into account (liquid boiling and evaporation).
Comments:
1. Model hypothesis & mathematical model.
The scheme of the cryogenic propellant tank should be presented for a better understanding of the model proposed.
2. Page 3, line 96: “The pre-cooling liquid and gas inside the tank are uniform in temperature distribution and have no thermal stratification.”
No information regarding the liquid level in the tank or the time course of the liquid level in the tank is presented. No liquid volume is taken into account in the process model. Only gas volume was taken into account as follows from Equation (3).
3. Page 3, equation (2): cooling capacity required to lower the gas temperature in the tank
Equation (2) describes the indirect cooling of steady gas mass in the tank.
According to the manuscript, the liquid hydrogen is evaporated during pre-cooling.
In this case, the formed vapors are mixed with the present gas, in my point of view.
The following ambiguity is related to this liquid evaporation. Is the tank pressurized or is a constant pressure maintained and excess vapor does escape?
4. Page 3, Equations (2), (9), (10): mathematically incorrect notation
“dT - the temperature variation per unit time“ – the correct notation is „dT/dt“ in this case.
5. Page 4, Equation (12): unexplained symbols: Theta and V
a) Theta: tank evaporation rate: the quantity is not defined. It is not clear by which way this quantity was determined.
b) V - unexplained symbol. Probably, the letter V symbolizes liquid volume (but the symbol V was used for gas volume in Eq. (3))
c) rL – “propellant liquid concentration: I recommend using the term “ the propellant liquid density”.
6. Page 4, lines 160 and 167: tank evaporation rate vs. mass of pre-cooling medium required per unit time.
What is the difference between “tank evaporation rate” and “mass of pre-cooling medium required per unit time”? The values of the tank evaporation rate, measured (?) or calculated (?), are not presented in the manuscript.
7. Page 4: Evaporation rate and evaporated amount.
The evaporation rate depends on the boiling heat transfer coefficient, the contact area between the liquid and tank wall, and the temperature difference between saturated liquid temperature and wall temperature. Moreover, the boiling regime and boiling heat transfer coefficient consequently, depend on mentioned temperature difference also.
These factors affecting heat transfer during liquid boiling and evaporation are not discussed and taken into account in the model proposed.
Formal comments:
1) Page 9, table 2, column headings “ Luquid hydrogen mass flow” – printing error
2) Table 2: Joules – capital letter “J” should be used.
3) Figure 3: figure caption – “K/min” is correct
Author Response
Comment 1: Model hypothesis & mathematical model. The scheme of the cryogenic propellant tank should be presented for a better understanding of the model proposed.
Responses: Figure 1 is added as required，which shows the structure of liquid hydrogen storage tank and heat during precooling.
Comment 2: Page 3, line 96: “The pre-cooling liquid and gas inside the tank are uniform in temperature distribution and have no thermal stratification.” No information regarding the liquid level in the tank or the time course of the liquid level in the tank is presented. No liquid volume is taken into account in the process model. Only gas volume was taken into account as follows from Equation (3).
Responses: Section 2.1 describes the liquid phase change and storage conditions during the precooling process. Liquid hydrogen will be stored only when the bottom wall temperature is lower than the boiling point of liquid hydrogen. In the actual precooling process, the level of liquid hydrogen stored in 300m3 storage tank is very low. Considering the model simplification, it is feasible to ignore the liquid volume. A new hypothesis has been added to the Section 2.2.
Comment 3: Page 3, equation (2): cooling capacity required to lower the gas temperature in the tank. Equation (2) describes the indirect cooling of steady gas mass in the tank. According to the manuscript, the liquid hydrogen is evaporated during pre-cooling. In this case, the formed vapors are mixed with the present gas, in my point of view. The following ambiguity is related to this liquid evaporation. Is the tank pressurized or is a constant pressure maintained and excess vapor does escape?
Responses: The liquid hydrogen is evaporated during pre-cooling, and the formed vapors are mixed with the present gas. The tank keeps a constant pressure maintained in this case. The gas outlet of the storage tank is always open, excess vapor escapes and the pressure is 0.1Mpa during pre-cooling.
Comment 4: Page 3, Equations (2), (9), (10): mathematically incorrect notation. dT - the temperature variation per unit time – the correct notation is dT/dt in this case.
Responses: The manuscript has been changed as required.
Comment 5: Page 4, Equation (12): unexplained symbols: Theta and V.a) Theta: tank evaporation rate: the quantity is not defined. It is not clear by which way this quantity was determined. b) V - unexplained symbol. Probably, the letter V symbolizes liquid volume (but the symbol V was used for gas volume in Eq. (3). c) rL – “propellant liquid concentration: I recommend using the term “the propellant liquid density”.
Responses: a) Theta is the evaporation rate of the storage tank, and the quantity is derived from literature [20]; b) V is the tank volume, the gas volume in equation (3) and the liquid volume in equation (12)is equal to the tank volume; c）RL has been changed to "propellant liquid density".
Comment 6: Page 4, lines 160 and 167: tank evaporation rate vs. mass of pre-cooling medium required per unit time. What is the difference between “tank evaporation rate” and “mass of pre-cooling medium required per unit time”? The values of the tank evaporation rate, measured (?) or calculated (?), are not presented in the manuscript.
Responses: The main difference between the evaporation rate and the mass of the pre-cooling medium required per unit time is that the storage tank is in a different state. The former refers to the liquid evaporation rate under normal storage conditions, and the temperature of all structure materials in the tank is stable and cryogenic. The latter refers to the mass of liquid consumed in the pre-cooling process. The temperature of all structural materials is changing from normal to cryogenic. Evaporation rate of the 300m3 tank is listed in Table 1 which was derived from literature [20].
Comment 7: Page 4: Evaporation rate and evaporated amount. The evaporation rate depends on the boiling heat transfer coefficient, the contact area between the liquid and tank wall, and the temperature difference between saturated liquid temperature and wall temperature. Moreover, the boiling regime and boiling heat transfer coefficient consequently, depend on mentioned temperature difference also. These factors affecting heat transfer during liquid boiling and evaporation are not discussed and taken into account in the model proposed.
Responses: The evaporation rate really depends on the boiling heat transfer coefficient, the contact area and the temperature difference between the liquid and the tank wall. In engineering applications, the cooling rate of the storage tank is determined in advance. This manuscript simplifies the model by assuming several cooling rates similar to the actual engineering, which satisfies the conditions to calculate and analysis the liquid hydrogen consumption and the proportion of various heat loads under different cooling rates. The effect of the evaporation rate of liquid hydrogen in the precooling process is implied in the assumed cooling rate. Therefore, these factors affecting liquid boiling and evaporation are not taken into account in the simplified model.
Comment 8: Formal comments:
1) Page 9, table 2, column headings “ Luquid hydrogen mass flow” – printing error
2) Table 2: Joules – capital letter “J” should be used.
3) Figure 3: figure caption – “K/min” is correct
Responses: The manuscript has been changed as required, and the vertical axis unit in Figure 2 has been modified additionally.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
Accept as it is
