Mathematical Modelling of a Propellent Gauging System: A Case Study on PRISMA
Steven Collicott
Round 1
Reviewer 1 Report
This paper details a comparative study on propellant gauging methods, as applied to the PRISMA mission.
- Can these gauging methods be effectively used with propellants which feature decomposition over life, such as hydrogen peroxide? Some commentary on the limitations of gauging would be interesting.
- In table 1 the nominal heater power is listed as 10 W. Was the avionics driver used capable of maintaining a 10 W power consumption, or was it simply a bus voltage applied to a resistive heating element? If the latter approach was used, the power consumption will vary as the element heats up (thus causing the resistance to change). This could have a substantial effect on the heat input to the system, and thus to the accuracy of the TGM gauging model.
- In equation 2 a coefficient of 0.0006564 is used in what appears to be an empirical fit to test data. In the differentials of equation 2 shown in equations 3 and 4, this coefficient has changed to 0.0044551. Can the authors detail the differentiation method used for equations 3 and 4 which would lead to this coefficient?
- In section 2.3 line 331 an average density of hydrazine is calculated. From data which I have available there appears to be a ~3% decrease in the density of hydrazine from 10 to 50 degrees. Would using a temperature corrected density allow for increased accuracy of the PVT model?
- Equation 16 has what appear to be radiative heat transfer terms included. However, heat transfer between the upper and lower tanks appears to have been neglected, and all bodies are treated as isothermal. The model also features Text used to represent what seems to be the external temperature of the spacecraft, rather than the external temperature of the tank defined in the nomenclature.
- Has a FE thermal model been considered to evaluate the scale of the contributions of radiative heat transfer to the heat loss of the system in vacuum?
- On line 397 the authors define the "actual propellant heat capacity" as the difference of the "actual heat capacity" and "true heat capacity" - this nomenclature is very confusing to the reader, and should be clarified.
- Figure 5 features negative Y axis values, representing negative estimated mass - this should be remarked upon in the text as a result which is obviously not realistic or useful.
- On lines 537-538 the authors comment on estimated mass decreasing from 0.7 kg to 1.02 kg, which is an increase.
- On lines 543-544 the authors comment on an error of 0.1 kg being "less by thermal propellant gauging" than an error of 0.1 kg, which is an error of equal magnitude.
- Figure 10 shows predictions by the TPG and BKP methods. The predicted envelopes diverge at higher burn times. Can the authors provide some commentary on which envelope would be anticipated to be the "true" envelope of the system? It may also be interesting to add the envelope of the PVT method to this figure.
- The paragraph commencing on line 551 should be clarified to state that it is referring to the magnitude of the error value.
- In the final bullet point before the conclusions, the authors state that use of the TPG model would allow extension of the PRISMA mission by up to 5 months. Can the authors comment on the potential risks to the mission of relying upon a less conservative (as shown in figure 10) gauging method?
There are some typos in the paper, along with a number of terms which are used in the text but not explained in the nomenclature. There are also some inconsistencies in the nomenclature used in places in the paper.
Author Response
Firstly, the authors would like to thank the editor and reviewers for their precious time and constructive suggestions. We have carefully addressed all the comments. According to the reviewers' comments, our response is summarized below, and the corresponding changes and refinements were made in the revised paper.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments on “Mathematical Modelling of Propellant Gauging System: A Case Study on PRISMA”
1. Overall an unique and interesting paper.
2. Lines 154 to 194: Here “TGM” and “Thermal Gauging Method” are discussed. It is my assumption that this is what is called “TPG” and “Thermal Propellant Gauging” elsewhere. If this is correct, then clean up the TGM instances, else if I’m wrong, please clarify differences between TPG and TGM.
3. Line 366: capitalize “Newton”
4. Section 2.4: you make no mention of the need to understand the spatial distribution of the liquid propellant inside the tank and propellant management device. Your reference 13 describes this. Are uncertainties in this liquid distribution in 3D in zero-g another source of uncertainty or are they captured in your existing uncertainties?
5. How many temperature sensors should be used and where should they be on the tank for doing TPG well or for making it even better?
6. Fig 8 slopes are nanoKelvins per second? That’s 0.03K per year, right? Reference 13 and Yendler’s later work (https://doi.org/10.2514/1.27818 ) show much faster heating, just a couple of days to get several Kelvin temperature changes. What’s the source of this apparent mis-match?
7. Line 518 you state that propellant temperature must be held constant, but then how do you heat it to get the slopes plotted in Figure 8?
8. Is unclear to me if the PVT analysis includes tank bulge with pressure and solubility of the pressurant gas in the hydrazine.
9. Reference 31 duplicates reference 13?
Author Response
Firstly, the authors would like to thank the editor and reviewers for their precious time and constructive suggestions. We have carefully addressed all the comments. According to the reviewers' comments, our response is summarized below, and the corresponding changes and refinements were made in the revised paper.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The authors have adequately responded to my queries from my first review. I believe that the updated paper is now fit for publication.
