Experimental Study on the Mass Flow Rate of the Self-Pressurizing Propellants in the Rocket Injector

Round 1

Reviewer 1 Report

Dear authors,

 

This paper shows how the length of injector effects the flow regime and mass flow rate of nitro oxide as a self-pressurization oxidizer with the experiments. It is very important topics for hybrid rocket with nitro oxide. You showed some experimental results, and I can evaluate them highly. However, there is a part that I cannot understand your assert due to lack of explanation of experimental equipment and methods, information on results using water, and explanation of interpretation of results. I think it is necessary to add more detail explanation and discussion in order to make readers to understand clearly. Please find my comments below:

 

1. You should show the size of the run tank and the chamber, and the inner diameter of the tubes.
2. Line 216. What is “the desired level”? How much did you fill nitrous oxide in the run tank? How much was the ullage volume in the run tank at each test?
3. How much were the temperatures of nitrous oxide at each position? I think that the temperature of nitrous oxide was decrease when the nitrous oxide vaporizes because of heat of vaporization. If the temperature changes, the boiling point also changes.
4. Around line 190-203. You should show the results of the tests with water. Time trace of load cell data, etc. I could not understand why you said the obtained mass flow data is reliable.
5. Figure 5 and 6. I did not understand why you considered that the liquid depletion is at about 88 s. From 88 to 91 s, the mass flow rate is still relatively higher. So, I think that liquid phase still exists. Of course, the rate of gas phase is increasing. Please explain more.
6. How did you estimate h1 and h2? I think h1 and h2 is changing during each test because the pressure and the temperature are changing with time. Please show the time trace of h1 and h2.
7. How did you estimate the bulk density in equation (4). Please show the time trace of the bulk density.
8. Equation (7). Why is the denominator “mv-ml”? Not “mt”?
9. In figure 10 and section 4. You mention the L/D effects the phase of flow. However, it is not sure because you did not change D. I can understand “L” (means residence time) effects the flow regimes. If you have any other evidence that “L/D” effects the flow regimes, please explain with the evidence.
10. As discussion, to clarify readers’ understanding, it is better to explain the mechanism that the residence time effects the flow regimes.
11. Line 385-387. You said that “For low L/D, the critical flow starts when the chamber pressure drops below roughly 60% of the vapor pressure, while for very high L/D, the critical flow starts below 75% of the vapor pressure.” Why does it happen? Please discuss more not only showing the result.

Author Response

 Thank you for your feedback. Please find our responses:

 

1. The run tank is fi40 mm internal diameter, 220 mm length. The chamber is fi40 mm internal diameter, 400 mm length. The inner diameter of the tubes is 4 mm.

2. The total volume of the run tank is about 0,28L. The typical initial mass of the nitrous oxide filled in the run tank was 180-190 g. This gives ullage volume of about 15%.

3. Yes, you are right. The temperature drops significantly at points where evaporation is the highest, mostly at the Injector, but also it can be seen in the run tank. We have no direct measurement of the temperature of the flow, only rough measurements of the external structures.

4. We will include the result for the water test that shows the comparison between measured mass flow rate on the setup and using the flowmeter. It supports the reliability of the measurements.

5. You are right, that the liquid depletion point cannot be determined only by looking at the graph. Especially because there is no sudden evaporation of all the liquid, an only smooth increase of the gas phase, and finally, no liquid is present.

   The choice of depletion point has also been supported by plotting the entire mass flow rate curve vs pressure drop, without trimming. There in the SPI region can be seen that flow deviates from the SPI curve, at some low dP, which is adequate for the dP in Figure 6. It is familiar behavior known from the hybrid engines, where there is a shift in the engine performance at the liquid depletion by the end of the test. Additionally, the weight of the run tank at the depletion point is some clue. Obviously, it cannot be determined conclusively that there is no liquid present at this point. However, since the focus of this paper is more on the critical flow and regions where the liquid flow is present, there is no need to include gas region in the analysis, as it does not bring any value to the paper.

6. We have not measured temperature to estimate enthalpy. That is correct that h1 and h2 are changing with time. To calculate the curves from the test data for the HEM model, we have used pressure P1 and assumed that the nitrous oxide is saturated and in equilibrium. This is obviously not valid, but those are assumptions for the HEM model, and that is often how the model is used in practice.

7. The bulk density at point 2 (downstream of the Injector), for the HEM model, has been estimated from the enthalpy and pressure at point 2. The pressure has been measured, while the enthalpy has been calculated using the constant entropy assumption from point 1 to point 2 (s1 = s2). This is in line with the HEM model assumptions.

8. Thank you for pointing that out. The denominator is correct, but the left-hand side should be α (void fraction), not QF. It is a result of substituting Eq. 6 to Eq.5, and solving for alpha. Then, the QF is calculated using x = 1 / (1 + ((1-alpha) / alpha) * (rho_l / rho_v)).

9. That is correct, we have not varied D, so that only from these results the effects of L/D cannot be determined. However, the L/D is known in the literature to have such effects as we have found, including the studies on the nitrous oxide or analogous carbon dioxide. We would add citations to support the L/D evidence and remark that our results clearly show the length's effect, but the diameter has not been varied.

10. We will add more discussion on this.

11. It is related to the residence time and pressure drop (here, pressure drop is Pv – P2). The higher the residence time and pressure drop the better the two-phase flow develops, at some point “chocking” the orifice so that mass flow reaches its maximum. Above this point the mass flow is independent of the pressure drop, so it is independent of the ratio of chamber pressure P2 and vapor pressure Pv. Since larger L/D increases residence time, the orifices with high L/D reach the chocking point for smaller pressure drop or P2/Pv ratio. We will add more discussion on this.

    
    

     

Reviewer 2 Report

In the paper very simplified analyses of the mass flow rate of the self-pressurizing nitrous oxide, in injector. It is only limited to the nitrous oxide, not generally rocket propellants, so the title of the paper have to be modified.

The analyses is rather simple, but for students experiments, it may be justified. This however, do not justify some assumptions and clarity of presentation of the results.

In the paper also analyses of the error have to be presented. Only on line 377 is stated “Using Cd (water) for each injector, the predicted critical mass flow rate was in ± 10% error margin”. On what bases  ± 10% error was estimated? It must be supported by the error calculations which should be based on errors of all measurements sensors used for mass flow calculations.

Additionally it will be much better to shown schematic diagram of the test system with elements indicated on the diagram and picture (actually shown in Figure 1) can be only addition to the schematic diagram.

On line 143 instead of “straight orifice with the square edge of the same diameter (1.5 mm) but varies”, should be “straight orifice with the sharp edge of the same diameter (1.5 mm) but varies”??

It will be much better when in all Figures where time is a parameter  “Time” should  start from “0” at beginning of experiment (it is really very easy to recalculate) and will be more clear for reading/analyses.

On line 275-276 Initial temperature and vapor pressure of the saturated nitrous oxide in the storage tank and the run tank have been kept at roughly Pv= 52 bar. This pressure is only initial and during runs/experiments vaper pressure of the nitrous oxides is different – is no longer saturated, so there are no sense to compare pressure ratios to saturated pressure, since no longer such pressure exist in tank/before injector during whole experiment!

On line 385 it is stated “P2 P1 ⁄, which seems to depend on the L/D ratio, as shown in Figure 10”, but in Fig.10 there is relation to “critical flow transition P2/Pv”. Why not P1/P2? Please explain!

It is difficult to analyze graphs as a function of the reciprocal of pressure ratio. It is not understandable – it should be always as the function of pressure ratio ( pressure ratio/pressure drop are the major factor of mass flow rate)

Equation (4) for mass flow ṁHEM is only valid for ideal gases!!, so why it is used for two-phase flow? It is a not justified assumption. It is only justified for IDEAL GASES!!!

Author Response

Thank you for your feedback. We will adapt the suggestions, particularly the error calculations, and time parameter starts from 0 on Figures.

The pressure ratio P2/P1 has been used following convention by some other papers in the same subject e.g. Waxman et al. (2013). Mass flow rate and isolation characteristics of injectors for use with self-pressurizing oxidizers in hybrid rockets. 49th AIAA/ASME/SAE/ASEE Joint Propulsion Conference. It is understood that the reciprocal gives the same conclusions.

The Pv has been used interchangeably with P1 in some parts of this paper. Pv will be replaced with P1 in proper Figures. While this is obviously not correct, the goal of this paper was to compare experimental data with two popular and simple flow models: SPI and HEM. Their assumptions include that the fluid is in equilibrium and is saturated. That is why in the calculations, Pv = P1. Physically, it is not valid, but the paper follows this simplification commonly made in engineering practice. The same is true with the HEM model. It is not valid for this case of the two-phase model, while still it is used in practice with success.

Reviewer 3 Report

The paper is surely intersting as the experiments are more systematic than previous reserches except for Waxman that, however, didn't consider the case without supercharging, which is probably the more frequent for typical hybrid sounding rockets.  I suggest to improve the introduction/references both in general about self-press nitrous oxide hybrids/liquids and in particularly regarding the topic of injector mass-flow. For the latter, for example:

Whitmore et al. "Engineering Model for Self-Pressurizing Saturated-N2O-Propellant Feed Systems 

Stannard et al. "Experimental investigation of self-pressurized propellant injection into a simulated rocket motor combustion chamber"

Paccagnella et al. "CFD Simulations of Self-Pressurized Nitrous Oxide Hybrid Rocket Motors"

Some of the previous references seem to stretch the fact that the HEM model tends to significantly underpredict the mass flow even in chocked conditions while in this paper the results are ok (however I have to say that I performed a similar unpublished experiment and also in my case the HEM was pretty good particularly at large L/D). The authors shoul try to expand the comparison/explanation with the previous references.

Another question: why in Figure 8 the "knees" have this behaviour? For example injector 5 has a region of higher mass flow around the critical DP? Why the starting DP of the graphs is not the same for all the injectors? Only for injector 5 is near zero. Is it possible that for some reasons (experimental errors or whatever) in Figure 9 the curves are shifted to the left for lower L/D?

Author Response

 

Thank you for your feedback. We will include more references and improve the introduction to provide more information about self-pressurizing nitrous oxide rockets and injector mass-flow. We have also noticed that the literature reports that the HEM model underpredicts significantly. However, in our previous work with small-scale hybrids and liquids, we have noticed that we got very good results under some conditions (mainly L/D) with HEM. We have noticed that there were not that many experiments with the flow of self-pressurized nitrous oxide. That is one of the motivations to check that more deeply. We will try to include more comparisons of our results with previous references.

 

As to the “knees” on Figure 8 we are not entirely sure what is the reason for this behavior. Since we have not seen similar behavior in other references and our previous work, we believe that is the residue from the mass measurement method. The mass rate signal has more vibration at the initial approx. 2 seconds of the test, during which the critical point is usually reached. This adds some uncertainty to this region.

 

The DP range (for liquid flow) for each test is slightly different. It depends on several factors like initial conditions (fill level of the run tank) or the rate of the pressure build-up in the chamber. We believe that both these factors contributed to the injector 5 curves. The exhaust valve for the chamber has been used to find the test conditions so that we obtain the DP region between 5 – 30 bar, where the interesting behavior takes place.  We do not see any reason for that the curves in Figure 9 are shifted, except that it is a result of the flow for each Injector.

Round 2

Reviewer 1 Report

Thank you for the explain against my question and modification of the paper.
The revised paper clarify experimental conditions, focus, interpretation of results, and authors' considerations.
Now I understand well and I think readers can understand your considerations.
Therefore, I accept to publish your paper.

Author Response

Dear Reviewer,

thank you for your kind feedback.

Best regards,

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

This work is dealing with the characteristics of the flow rate of two-phase N2O with respect to the pressure loss of the orifice-type injector being used for supplying the propellant to a combustion chamber from a self-pressurizing tank in hybrid rockets, etc., as well as the orifice L/D dependence. This is an attempt to experimentally evaluate using instantaneous mass measurement, verify the prediction method based on the conventional liquid flow and equilibrium two-phase flow theories, evaluate the design method, and give new recommendations. It provides new experimental data and is an important task with scientific content worthy of publication. However, on the other hand, regarding the current description, it is necessary to proof-read English expressions by native speakers, and there are many parts that require more accurate description and easy-to-understand description of the content. So, I would like to judge later again the adoption or rejection of this work after some major revision will have been made. Below is a list of the parts that my concerns are in.

Line 63: have to write here what the HEM stands for.

Lines 84-90: A little more detail description is wanted on what the differences between self-pressurization and external pressurization are? Can you give actual examples of how different phenomena and behaviors occur? It seems to be useful for appealing the significance and necessity of this work.

Lines 101-105: Please use the numbers shown in the figure in texts also to help understanding.

Lines 104-105: Please clarify which valve is “the valve”. Please indicate "the flexible tube" by a number used in the figure.

Line 107: What is “the storage tank”? Can it be shown in the figure? Is it different from "the run tank"? Please clarify it. Which is "the flexible tube" here? Please show it in the figure. Please clarify whether this is "the flexible tube" in line 105.

Lines 107-110: The explanation is difficult to understand, so please rewrite it in an easy-to-understand manner.

Lines 125-127: “To make sure ~ downstream chamber.” please explain this in more detail. Does the injector in Figure 2 (a) correspond to No. 3? Or is it No. 1 or No. 5? How are the shapes of No. 1 to No. 5 injectors different?

Lines 140-142: The Coriolis flowmeter cites "due to the undetermined two-phase transients" as the reason for "unreliable readings". Please explain this a little more why the Coriolis flowmeter is so.

Lines 148-150: What kind of work is “a significant amount of work”? Is it described in this treatise? Or is there already a report?

Lines 158-160: please illustrate.

Lines 162-166: Please explain in a little more detail for better understandings. Why does this method give good results?

Lines 168-172: How did you verify that this measurement method could be used? Why can we evaluate the characteristics of the two-phase mass flow rate when the problems of mechanical coupling and differentiation remain? Please explain more for better understandings.

Line 175:  Another 2.1, maybe 2.2?

Lines 180-182: It is hard to understand the explanation here. Please explain more for better understanding.

Lines 188-199: Please explain it, using the example of Figure 3, in a sequence of the time with the time level apparently shown.

Line 230: Is the mass flow rate a red curve? Please describe it in Figure 6.

I would like you to show the measurement error of the mass flow rate by evaluating the error propagation from the measurement error of the weight, which is the measurement data and the differentiation with respect to the time.

Line 231 Please define clearly the "mass flow rate transition", so that it can be "clearly identified”.

Line 279: Please indicate the evaluation error of Critical ΔP and critical m_dot.

Line 311: Not every reader always know S = 1 means. so please explain exactly what "flow without slip" means.

Lines 317-318: Please explain why if QF> 0, it is reasonable for Cd (SPI) to decrease or there is a reason to say “these values correlate well with”.

Lines 329-330: What is literature reference?

Line 338: Clarify what kind of relationship “This relationship” means?

Line 341: Another 4..   maybe 5.?

Reviewer 2 Report

This study presents effects of the two-phase N2O flow on the mass flow rate through the experimental methods. Summarized results show the interesting trends compared with two analytical models, SPI and HEM. However, there are very critical questions about the experimental conditions and authors’ assumptions related to the induced conclusion.

1. In this study, the tank is not over-pressurized. After the valve opens, the tank pressure immediately drops below the vapor pressure. Then the flow will boil from the tank and the flow phase is hard to know in the supply lines. Accordingly, it’s questionable that the two-phase flow exists in the whole system. Authors have to check the phase diagrams at three measuring points, Pt, P1 and P2.
2. Even when the two-phase flow occurs, it’s the problem to estimate the effect of injector geometry on the results because the upstream flow phase continuously changes in time. Thus, the design of the experiment is wrong. The tank should be over pressurized and the injection pressure has to be precisely controlled as the steady state.
3. Authors’ assumed the constant discharge coefficient (Cd) for all injector types, as 0.9. But an orifice with the longer L/D must have the larger pressure loss and this affects the Cd directly. In addition, the Cd changes as the pressure drop changes with the same geometry. Then this Cd can affect the results of the critical points. Authors have to explain the assumption of constant Cd for all injectors clearly.
4. From Line 71, authors mentioned that the accuracy of the HEM model is related to the residence time and L/D of the injector. However, as shown in Figure 8, the accuracy of the HEM model is related to the injection pressure drop, not to the injector types. What is the reason for this phenomenon?
5. Authors mainly use the injection pressure drop as the main parameter in this study. However, the phase of flow depends on the pressure and temperature at each location. It means that the injection pressure and the chamber pressure are more important to determine the flow phase at the orifice. If the chamber pressure which is the back pressure of the orifice is too low, the flow evaporates rapidly inside the orifice. It means that the phase of flow can differ with the pressure conditions at upstream and downstream of the orifice even though the pressure drop is the same. It’s really important to keep the same pressure conditions and just change the pressure drop of the injector with injector geometry changes if authors want to use the injection pressure drop as the main parameter. Therefore, Figure 8 can be explained as follows,
6. When the valve just opened, the chamber pressure (back pressure) is low. Then the N2O highly evaporates at the orifice and the orifice is choked. This flow is presented in Figure 8 from the pressure drop of 35 bar to 15 bar.
7. After some seconds, evaporated gases fill the chamber and the back pressure increases. At the specific point, the chamber pressure increases enough and the flow changes to the two-phase flow. This flow is presented from 15 bar to 0 bar.

Thus, it is not sure that the whole experimental conditions are in the two-phase flow conditions. And the results would be derived by the chamber pressure not by the pressure drop.

In conclusion, it is suspicious if the experiment was well designed as authors intended. The assumptions and analyses of results are not acceptable enough based on this experiment. Therefore, in spite of the scientific importance of the topic, this manuscript is not acceptable for now.