Performance and Modeling of a Two-Stage Light Gas Gun Driven by Gaseous Detonation

Round 1

Reviewer 1 Report

Page 4: In equation 1, the value of R_pro is given as 30mm, but what is value for R_red that you have used?

 

Page 5, Figure 4 caption. The velocity of 2481 m/s is given for the projectile – later in the manuscript you show how this velocity varies with time (and therefore distance along the launch tube) – can you make it clear at which location this velocity is being measured? I assume it’s through an optical window in the target chamber?

 

Page 6, line 227: In the T’ = 0.9T + 0.03M^2T + 0.46Tw equation, what is M?

 

Page 6, line 230 – the equation for the viscosity reads mu’ = mu’(T’, rho’), should this be mu’ = mu(T’, rho’)?

 

Page 7, line 264 states that the Equations 10, 11, and 12 are solved, but above it is stated that Equation 11 = 0. Can you provide more detail on the radial stress is solved for?

 

Page 8, line 269, typo in spelling of the word ‘piston’

 

Page 8, line 293 – why did the experiment fail to capture the projective velocity for Case 3?

 

Page 9, line 322, should Figure 7 on this line read Figure 8?

 

Page 10, Figure 8 – it is stated that the diaphragm II ruptures at 82.8 ms. If the diaphragm has not yet ruptured, why is the pressure at the base of the projectile, which is downstream of the diaphram, already increasing before 82.8 ms? Would this happen in the experiment or is it something to do with how the numerical model is set up?

 

Pages 11 and 12 – you have two Figures labelled at Figure 10.

Author Response

Dear Editor and Reviewers:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Performance and modeling of a two-stage light gas gun driven by gaseous detonation” (Manuscript ID: applsci-818757). Those comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and have made correction which we hope meet with approval. The corrections are highlighted in the file “Marked manuscript”, and the responds to the reviewer’s comments are as flowing:

 

Page 4: In equation 1, the value of R_pro is given as 30mm, but what is value for R_red that you have used? 

Edge detection and shape fitting methods were applied in the present study to calculate the velocity of the projectile. Thus, R_red and Δd represent the radius of the red circle and the distance between the center of the red circle in two images. They have the unit of pixel and their values are related to the resolution of the high-speed camera. However, their values are detected from the images and have no influence to the actual projectile velocity.

 

Page 5, Figure 4 caption. The velocity of 2481 m/s is given for the projectile – later in the manuscript you show how this velocity varies with time (and therefore distance along the launch tube) – can you make it clear at which location this velocity is being measured? I assume it’s through an optical window in the target chamber?

The projectile speed was actually obtained through the optical window 3320 mm away from the muzzle exit.

The projectile speed varies with the distance along the launch tube. However, its speed was assumed constant in the target chamber since the pressure in the chamber was set to a low pressure in the order of several kilo pascal. We add explanations in the revised manuscript and hope the discussion is sufficient enough to meet the requirements of the reviewer.

 

Page 6, line 227: In the T’ = 0.9T + 0.03M^2T + 0.46Tw equation, what is M?

M is the Mach number and its definition has been added in line 228 in the revised manuscript.

 

Page 6, line 230 – the equation for the viscosity reads mu’ = mu’(T’, rho’), should this be mu’ = mu(T’, rho’)?

 only means that μ’ is function of T’ and ρ’. We use this equation as it was already used in Ref.12. And it has no influence to our result in the present manuscript.

 

Page 7, line 264 states that the Equations 10, 11, and 12 are solved, but above it is stated that Equation 11 = 0. Can you provide more detail on the radial stress is solved for?

Indeed, we made a mistake that the ε_θ is equal to 0. The formula and results has been corrected in the revised manuscript.

 

Page 8, line 269, typo in spelling of the word ‘piston’

It has been corrected in line 269 in the revised manuscript.

 

Page 8, line 293 – why did the experiment fail to capture the projectile velocity for Case 3?

For Case 3, it’s a special experiment to investigate the MHD effect for hypersonic flows. A magnetic sphere was installed in the projectile and the projectile was broken seriously during the acceleration process. We attribute it to the gap between the filling material and the projectile or the excessive internal stress larger than the projectile material strength due to the impedance mismatch. Thus, the experiment failed to capture the projectile velocity this time. However, we think the present work is okay to validate the numerical method since the piston velocities and pressure distributions agreed well with the experimental ones for all the cases. We will improve the present experimental work in the future.

We hope the discussion is sufficient enough to meet the requirements of the reviewer.

 

Page 9, line 322, should Figure 7 on this line read Figure 8?

It’s a typo and has been corrected in line 322 in the revised manuscript.

 

Page 10, Figure 8 – it is stated that the diaphragm II ruptures at 82.8 ms. If the diaphragm has not yet ruptured, why is the pressure at the base of the projectile, which is downstream of the diaphragm, already increasing before 82.8 ms? Would this happen in the experiment or is it something to do with how the numerical model is set up?

The pressure at the base of the projectile was actually the pressure on the diaphragm surface before 82.8 ms. In this quasi-one-dimensional numerical model, the diaphragm rupture process was not considered in the simulation. The diaphragm was assumed to be ideally open instantaneously. Since the projectile was placed close to diaphragm II, we use this pressure to monitor the pressure on diaphragm II or the pressure histories at the base of the projectile at the same time. We add explanations in the revised manuscript.

 We hope the discussion is sufficient enough to meet the requirements of the reviewer.

 

Pages 11 and 12 – you have two Figures labelled at Figure 10.

The number of the figures have been corrected and checked carefully in the revised manuscript.

Author Response File: Author Response.docx

Reviewer 2 Report

A two-stage light gas gun driven by gaseous detonation was newly constructed, which can make up for the disadvantages of the insufficient driving capability of high-pressure gas and the constraints of gunpowder. The performance of the gas gun was investigated through experiments and a quasi-one-dimensional modeling of it was also developed and described in detail. The model accounts for the friction and heat transfer to the tube wall for gases by adding a source term. The paper presents both theoretical and experimental data.

Paper needs major revision prior to being considered for publication.

1. Authors state that “an improved model has been established to consider the inertial loads in the piston or projectile and model the friction force with the tube wall”. However, analyzing formulas (13), (14), (15) I should say that Authors seem not to take into account the distribution of the axial load in the piston between P_b and P_f. The distribution of load will bring to the distribution of normal load on the barrel in accordance with Hook’s law, and the last will cause the distribution of wall friction force between the piston and the barrel. Thus, friction force F should be the integral of local friction forces.
2. The onset of detonation in the combustible mixture is not a straight-forward process, and it has many alternative scenarios. ([1] N.N. Smirnov, V.F. Nikitin, Yu.G. Phylippov. Deflagration to detonation transition in gases in tubes with cavities. Journal of Engineering Physics and Thermophysics, 83, 6 (2010), pp. 1287-1316. ). ([2] V.F. Nikitin, V.R. Dushin, Y.G. Phylippov, J.C. Legros, Pulse detonation engines: technical approaches, Acta Astronaut. 64(2009) 281–287). Authors should bdescribe in details their model for detonation onset: do they assume that detonation wave lives the ignition tube and travels in the chamber, or do they have an assumption that the detonation wave onset takes place somewhere in the beginning along the whole surface of the chamber cross-section. Or some model for deflagration to detonation transition is used. The problem statement should be precise incorporating initial and boundary conditions as it was the case in the papers [1, 2].
3. The paper relying heavily on experimental studies is expected to provide detailed description of the precision of obtained results. The sufficient data should be provided on the errors of measurements, data processing, etc. The experimentally obtained values depicted in figures 5 and 7 should have bars in both directions indicating the possible deviation of measured parameter value.
4. Paper relying on data of numerical simulations should provide data on numerical error accumulation. The data on grid convergence study and experimental validation is not sufficient for reliable use of numerical predictions.

Providing the data of numerical results it is necessary providing the data on:

1)code validation – comparison with experimental data on some close problem – this comparison validates the mathematical model itself;

2) code verification – comparison with some exact analytical solution, or with numerical solution of some benchmark problem – this comparison verifies the numerical software, if it operates correctly;

3) grid independence study – this study testifies the grid size is sufficient providing necessary accuracy for some test problem;

4) accumulation of error estimates – provided for particular problem under consideration. . I should mention, that accumulation of errors is relevant to solving particular problem. The model (explicit dynamic codes) can be well validated, and the grid independence proved, nevertheless, accumulation of errors takes place at each integration step due to final size of a cell. The solution converges to the exact for cell size tending to zero. However, for final cell size the error itself depends on accuracy of algorithm and grid, and on the number of integration steps. Thus using the same code, but different number of integration steps in the algorithm, it is possible obtaining either reliable or unreliable results by the end of computations.  The method for accumulation of errors estimations being the function of timesteps is described, for example in the papers ([3] Smirnov, N.N., Betelin V.B., Nikitin, V.F., Stamov, L.I., Altoukhov, D.I. Accumulation of Errors in Numerical Simulations of Chemically Reacting Gas Dynamics. Acta Astronautica, 117 (2015), 338-355.  [4] N.N.Smirnov , V.B.Betelin, R.M.Shagaliev, V.F.Nikitin, I.M.Belyakov, Yu.N.Deryuguin, S.V.Aksenov, D.A.Korchazhkin. Hydrogen fuel rocket engines simulation using LOGOS code. International Journal of Hydrogen Energy. (2014), vol. 39, 10748-10756. ). Authors should provide relevant comments on their results.

 

Author Response

Dear Editor and Reviewers:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Performance and modeling of a two-stage light gas gun driven by gaseous detonation” (Manuscript ID: applsci-818757). Those comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and have made correction which we hope meet with approval. The corrections are highlighted in the file “Marked manuscript”, and the responds to the reviewer’s comments are as flowing:

 

Comments and Suggestions for Authors

Paper needs major revision prior to being considered for publication.

1. Authors state that “an improved model has been established to consider the inertial loads in the piston or projectile and model the friction force with the tube wall”. However, analyzing formulas (13), (14), (15) I should say that Authors seem not to take into account the distribution of the axial load in the piston between P_b and P_f. The distribution of load will bring to the distribution of normal load on the barrel in accordance with Hook’s law, and the last will cause the distribution of wall friction force between the piston and the barrel. Thus, friction force F should be the integral of local friction forces.

This is a valuable advice to improve our work. 

We totally agree that it would be better to take into account the distribution of the axial load instead of the stress in a certain plane of the piston. The axial stresses within a piston in arbitrary motion are uniform and are obtained by summing the static contribution and the simplified dynamic one, as displayed in eq. (9). However, the actual stress distribution in the piston is complicated and difficult to measure in our experiments. Besides, other factors, such as roughness of the tube wall, improper data on the high strain rate deflection and yielding behavior of the piston material, melting of the piston under high temperature environment, are all hard to estimate and neglect in our calculations. Thus, we just use eq. (9) for simple in our calculations and good agreements are still obtained. We will continue this work and make improvement in the future.   We hope the discussion is sufficient enough to meet the requirements of the reviewer.

 

2. The onset of detonation in the combustible mixture is not a straight-forward process, and it has many alternative scenarios. ([1] N.N. Smirnov, V.F. Nikitin, Yu.G. Phylippov. Deflagration to detonation transition in gases in tubes with cavities. Journal of Engineering Physics and Thermophysics, 83, 6 (2010), pp. 1287-1316. ). ([2] V.F. Nikitin, V.R. Dushin, Y.G. Phylippov, J.C. Legros, Pulse detonation engines: technical approaches, Acta Astronaut. 64(2009) 281–287). Authors should describe in details their model for detonation onset: do they assume that detonation wave lives the ignition tube and travels in the chamber, or do they have an assumption that the detonation wave onset takes place somewhere in the beginning along the whole surface of the chamber cross-section. Or some model for deflagration to detonation transition is used. The problem statement should be precise incorporating initial and boundary conditions as it was the case in the papers [1, 2].

The detonation driver has already been applied to shock tunnels successfully and its detonation onset has been described in many references related to detonation shock tunnels. Instead, detonation is just used a driver in our facility and we do not focus on its combustible processes. We add expiations in the revised manuscript and hope the discussion is sufficient enough to meet the requirements of the reviewer.

“The mixture in the ignition tube is initially ignited by electrical sparks. A high-temperature jet is formed and propagating into the driving section, thereby igniting the detonable gas directly. This will lead to a stable detonation wave traveling downstream in the detonation tube, behind which a Taylor wave follows and the products are at high temperature and pressure.”   

 

3. The paper relying heavily on experimental studies is expected to provide detailed description of the precision of obtained results. The sufficient data should be provided on the errors of measurements, data processing, etc. The experimentally obtained values depicted in figures 5 and 7 should have bars in both directions indicating the possible deviation of measured parameter value.

We think that we need lots of experimental results to show the exact error bars for the measured parameter value. However, the facility was newly built and the present numerical method was developed to model the results or explain the dynamic processes within the tube. We also tried to develop this simple method for the identification and assessment of new operating parameters of the test conditions without risk to the facility and hardware, as well as for the validation of new design concepts. We thought that the present work is okay to achieve this goal since the piston/projectile velocities and pressure distributions agreed well with the experimental ones. We will increase the experimental results and improve the present work continually in the future.    We hope the discussion is sufficient enough to meet the requirements of the reviewer.

 

4. Paper relying on data of numerical simulations should provide data on numerical error accumulation. The data on grid convergence study and experimental validation is not sufficient for reliable use of numerical predictions.

Providing the data of numerical results it is necessary providing the data on:

1)code validation – comparison with experimental data on some close problem – this comparison validates the mathematical model itself;

2) code verification – comparison with some exact analytical solution, or with numerical solution of some benchmark problem – this comparison verifies the numerical software, if it operates correctly;

3) grid independence study – this study testifies the grid size is sufficient providing necessary accuracy for some test problem;

4) accumulation of error estimates – provided for particular problem under consideration. . I should mention, that accumulation of errors is relevant to solving particular problem. The model (explicit dynamic codes) can be well validated, and the grid independence proved, nevertheless, accumulation of errors takes place at each integration step due to final size of a cell. The solution converges to the exact for cell size tending to zero. However, for final cell size the error itself depends on accuracy of algorithm and grid, and on the number of integration steps. Thus using the same code, but different number of integration steps in the algorithm, it is possible obtaining either reliable or unreliable results by the end of computations.  The method for accumulation of errors estimations being the function of timesteps is described, for example in the papers ([3] Smirnov, N.N., Betelin V.B., Nikitin, V.F., Stamov, L.I., Altoukhov, D.I. Accumulation of Errors in Numerical Simulations of Chemically Reacting Gas Dynamics. Acta Astronautica, 117 (2015), 338-355.  [4] N.N.Smirnov , V.B.Betelin, R.M.Shagaliev, V.F.Nikitin, I.M.Belyakov, Yu.N.Deryuguin, S.V.Aksenov, D.A.Korchazhkin. Hydrogen fuel rocket engines simulation using LOGOS code. International Journal of Hydrogen Energy. (2014), vol. 39, 10748-10756. ). Authors should provide relevant comments on their results.

This is really a challenging question for us.

We totally agree that numerical results rely on many influencing factors, like the grid size, algorithm, boundary conditions and so on. All these parts need detailed investigation. Grid independence or algorithm independence for a specific issue all need to be considered. These are almost the same situation for experimental works. We need to calibrate each pressure sensor, calibrate the size or weight of the projectile or piston. Thus, each part needs detailed consideration in our work.

In the present study, a new large two-stage gas gun driven by detonation was built and numerical method was developed to model the results or explain the dynamic processes within the tube. We also tried to develop this simple method for the identification and assessment of new operating parameters of the test conditions without risk to the facility and hardware, as well as for the validation of new design concepts. We thought that the present work is okay to achieve this goal since the piston/projectile velocities and pressure distributions agreed well with the experimental ones. We also displayed the detailed experimental or numerical processes.

Our numerical method was first developed in our previous paper (Ref. 23) using Euler equations. And the code was already validated through a high pressure or detonation one-stage gas gun. In the present study, viscous term was added for improvement. And it showed good agreement. Besides, shock tunnel driven detonation was developed and used in our institute for many years and the code for shock tunnels has been developed and validated for many cases. We believe that our code was reliable to be applied in the present investigation.

As for this manuscript, we thought that we achieved our goal and explained the results clearly. And of course, we will continue this work and make further improvement. We hope the discussion is sufficient enough to meet the requirements of the reviewer.

        

Author Response File: Author Response.docx

Reviewer 3 Report

 

Submitted paper deals with very interesting area - i.e. numerical and experimental investigations of two-stages light gas gun. Presented simplified numerical model ensured efficiency and satisfactory agreement with really impressive experiments, which was really nice for me, but I have several doubts about the numerical model applied in the paper:

1) In my opinion paper needs slight proofreading - especially in order to eliminate typos - e.g. line 269 ("piton");

2) References should be additionally checked - e.g. Ref. 11 does not include Eq. (5) - this relation is included in Ref. 12;

3) Cell velocity or cell temperature can be replaced by cell-averaged gas velocity / temperature (in presented model there is no cell motion - the eulerian approach was applied) - it is only suggestion;

4) In line 225 τ denotes stress - not force - compare with lines 194-195;

5) Moreover relation for τ in line 225 seems to be wrong (compare it carefully with Ref.12);

6) System of equations (2) also needs to be corrected (compare it carefully with Ref.12);

7) It would be good to insert citation of [12] in line 190 - eq. (5) seems to be cited from Ref.12;

8) The equation of motion (3) seems to be incorrect - was the friction force  added to the pressure force? That seems to be wrong;

9) In presented situation, the relation for q in line 231 is also inconsistent with system of conservation laws (2);

10) It would be better to use average stress inside the piston instead of maximum value - see eq. (9); As presented in the paper, the influence of this modification would be neglegible;

11) Eq. (10) and (11) describe strains - not stresses as mentioned in line 255;

12) Eq. (13) needs to be corrected - subscripts of pressure were accidentally omitted;

13) It would be useful to insert relative error in comparison with experiment in table 1;

14) Is the projectile mass correct in table 1? There is 100 g, which looks inconsistent with another values – probably it should be 10 g;

15) It would be useful to insert more experimental data points on the Fig. 7 - it would show function behaviour more accurately;

16) The Authors should insert information about rapture pressure for diaphragm I – only values for diaphragm II were given;

17) Some doubts are provided by information in line 260. As can be concluded, in the considered situation, the radial displacement of the material is present. So making use of relation describing the circumferential strain in cylindrical coordinates:

ε_θθ = (1/r )(∂u_θ/∂θ) + (u_r/r)

it can be observed, that this strain is different from zero (due to the radial displacement term). So the question is: why did Authors impose this strain component equal to zero?

18) In Fig. 5 the value of Δr for point d is equal to approx. 0.8 mm for steady state. It is difference in diameter or radius? In text there is an information about Δr = 0.25÷0.45 mm. The values on the Fig. 5 are twice larger;

19) In Table 1 the mixing ratio should be precised - is it volumetric or molar ratio?

20) The grid independence study should be improved. Calculations should be conducted for larger cell size. Applied values of Δx ensured no differences in results (Fig. 6), so it should be also calculated for larger value. Alternatively, there should be inserted table / figure with exact values of specific parameters (e.g. maximum pressure value) as the function of Δx;

21) The explanation of differences in Fig. 10 should be improved. As can be seen, sensor P3 ensured lower discrepancy between theory and experiment. What is the most important, P3 was exposed to the high temperature for longer time than P6, which gave larger discrepancy. So the explanation based on temperature influence does not seem to be reliable;

22) There is a mistake in the numbering of figures (Figure 10). 

I am looking forward constructive discussion in presented, very interesting area in order to improve the quality of works.

Kind regards

Author Response

Dear Editor and Reviewers:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Performance and modeling of a two-stage light gas gun driven by gaseous detonation” (Manuscript ID: applsci-818757). Those comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and have made correction which we hope meet with approval. The corrections are highlighted in the file “Marked manuscript”, and the responds to the reviewer’s comments are as flowing:

 

1) In my opinion paper needs slight proofreading - especially in order to eliminate typos - e.g. line 269 ("piton");

The word is a typo. We have checked the manuscript carefully and it has also been polished by a native English speaker.

 

2) References should be additionally checked - e.g. Ref. 11 does not include Eq. (5) - this relation is included in Ref. 12;

Yes, the equation was from Ref. 12 and it has been revised in the manuscript.

 

3) Cell velocity or cell temperature can be replaced by cell-averaged gas velocity / temperature (in presented model there is no cell motion - the eulerian approach was applied) - it is only suggestion;

Thanks for the suggestion. I have read many good references which are based on the Lagrangian formulation. And they are really helpful to develop our numerical code.

 

4) In line 225 τ denotes stress - not force - compare with lines 194-195;

The word has been corrected as ‘stress’ in the revised manuscript.

 

5) Moreover relation for τ in line 225 seems to be wrong (compare it carefully with Ref.12);

Although we have the different form in our manuscript, we have the same function. The relation in Ref.12 represents the wall-friction force and we use τ as the stress in a specific dx cell. Thus, we do not have dx in the equation.

 

6) System of equations (2) also needs to be corrected (compare it carefully with Ref.12);

It has been corrected in the revised manuscript.

 

7) It would be good to insert citation of [12] in line 190 - eq. (5) seems to be cited from Ref.12;

Although we have the same forms, our equation is not cited from Ref. 12. Equation (2) in the present paper involves a two-step chemical reaction model to simulate the detonation processes, where the equation in Ref. 12 involves the powder energy release.

 

8) The equation of motion (3) seems to be incorrect - was the friction force added to the pressure force? That seems to be wrong;

It’s a typo and the equation has been corrected in line 219 in the revised manuscript.

 

9) In presented situation, the relation for q in line 231 is also inconsistent with system of conservation laws (2);

This question is the same as we explained in question (5).

 

10) It would be better to use average stress inside the piston instead of maximum value - see eq. (9); As presented in the paper, the influence of this modification would be negligible;

We totally agree that it would be better to use average stress inside the piston. However, the actual stress distribution in the piston is complicated and difficult to measure in our experiments. Besides, other factors, such as roughness of the tube wall, improper data on the high strain rate deflection and yielding behavior of the piston material, melting of the piston under high temperature environment, are all hard to estimate take into account the distribution of the axial load. Thus, we just use eq.(9) for simple in our calculations and good agreements are still obtained. We will continue this work and make improvement in the future.

We hope the discussion is sufficient enough to meet the requirements of the reviewer.

 

11) Eq. (10) and (11) describe strains - not stresses as mentioned in line 255;

The statement of ‘stresses’ has been corrected as ‘strain-stress relationships’ in line 256.

 

12) Eq. (13) needs to be corrected - subscripts of pressure were accidentally omitted;

The subscripts have been added in the Eq. (13).

 

13) It would be useful to insert relative error in comparison with experiment in table 1;

The relative error has been added in the Table 1.

 

14) Is the projectile mass correct in table 1? There is 100 g, which looks inconsistent with another values – probably it should be 10 g;

We are sure that the projectile mass in Table 1 is correct. It is a relatively heavier projectile model in Case 2 in our experiment.

 

15) It would be useful to insert more experimental data points on the Fig. 7 - it would show function behavior more accurately;

We totally agree that it would be useful to insert more experimental data in our present study and show the error bars of the results at the same time. However, the facility was newly built and the present numerical method was developed to model the results or explain the dynamic processes within the tube. We also tried to develop this simple method for the identification and assessment of new operating parameters of the test conditions without risk to the facility and hardware, as well as for the validation of new design concepts. We thought that the present work is okay to achieve this goal since the piston/projectile velocities and pressure distributions agreed well with the experimental ones. We will increase the experimental results and improve the present work continually in the future.

We hope the discussion is sufficient enough to meet the requirements of the reviewer.

 

16) The Authors should insert information about rapture pressure for diaphragm I – only values for diaphragm II were given;

Diaphragm I, one of the most important components in this facility, separates the driver and driven section. It should be sure that its rupture pressure is larger than the initial filling pressure in the detonation tube. However, for a detonation driver, the pressure of the detonation products which breaks diaphragm I, are more than ten times of the initial pressure. Thus, we have a big margin for the burst pressure design of steel diaphragm I. We do not pay much attention to the exact burst pressure of diaphragm I, instead, it’s designed from our experience from detonation shock tunnel results. Unlike, diaphragm II, this value in fact has little influence to our results in the present study.   

We hope the discussion is sufficient enough to meet the requirements of the reviewer.

17) Some doubts are provided by information in line 260. As can be concluded, in the considered situation, the radial displacement of the material is present. So making use of relation describing the circumferential strain in cylindrical coordinates:

εθθ = (1/r )(∂uθ/∂θ) + (ur/r)

it can be observed, that this strain is different from zero (due to the radial displacement term). So the question is: why did Authors impose this strain component equal to zero?

Indeed, we made a mistake that the ε_θ is equal to 0. The formula and results has been corrected in the revised manuscript.

 

18) In Fig. 5 the value of Δr for point d is equal to approx. 0.8 mm for steady state. It is difference in diameter or radius? In text there is an information about Δr = 0.25-0.45 mm. The values on the Fig. 5 are twice larger;

The data in Figure 5 was actually the difference in diameter, where we use Δr in our calculations. And it has been corrected in Figure 5 in the in the revised manuscript.

 

19) In Table 1 the mixing ratio should be precised - is it volumetric or molar ratio?

It is molar ratio and it has been revised in Table 1.

 

20) The grid independence study should be improved. Calculations should be conducted for larger cell size. Applied values of Δx ensured no differences in results (Fig. 6), so it should be also calculated for larger value. Alternatively, there should be inserted table / figure with exact values of specific parameters (e.g. maximum pressure value) as the function of Δx;

The grid resolution with 60000 grids was used in the present study and the piston/projectile velocities and pressure distributions agreed well with the experimental ones. In fact, we have tried other grid resolutions before submitting the manuscript, such as 20000 or 90000 grids. However, we found no significant different between these grid resolutions for the issues that we concerned. Thus, only a grid convergence study for three different grid resolutions (40000, 60000, and 80000 grid points) was displayed in the manuscript and the difference is negligible as shown in Figure 6.  

 

21) The explanation of differences in Fig. 10 should be improved. As can be seen, sensor P3 ensured lower discrepancy between theory and experiment. What is the most important, P3 was exposed to the high temperature for longer time than P6, which gave larger discrepancy. So the explanation based on temperature influence does not seem to be reliable;

What we understand from the reviewer is the difference between CFD and Exp for P6 and P9 sensor after the passing of the piston. The reason may attribute to the inaccurate estimation of the energy exchange between the high temperature detonation gas (exceeds 3000 K) and the tube wall. This influence may go greater as time increases. It’s really difficult to give the exact heat transfer from the gas to the walls under such high temperature and high speed flow. We will go deeper investigation in the further. We add explanations in the revised manuscript.

 We hope the discussion is sufficient enough to meet the requirements of the reviewer.

 

22) There is a mistake in the numbering of figures (Figure 10).

The figures have been corrected in revised manuscript.

 

 

 

 

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Paper needed major revision prior to being considered for publication. The revised version incorporating Authors’ comments looks much worse. Details are below

1. Reviewer’s remark: Authors state that “an improved model has been established to consider the inertial loads in the piston or projectile and model the friction force with the tube wall”. However, analyzing formulas (13), (14), (15) I should say that Authors seem not to take into account the distribution of the axial load in the piston between P_b and P_f. The distribution of load will bring to the distribution of normal load on the barrel in accordance with Hook’s law, and the last will cause the distribution of wall friction force between the piston and the barrel. Thus, friction force F should be the integral of local friction forces.

The Authors’ reply:  

“…The axial stresses within a piston in arbitrary motion are uniform and are obtained by summing the static contribution and the simplified dynamic one, as displayed in eq. (9)...”  

Reviewer comment: The Authors’ statement is wrong. The distribution of axial stresses cannot be uniform in accelerated motion the pressures on both sides being different: P_b and P_f.

2. Reviewer’s remark: “The onset of detonation in the combustible mixture is not a straight-forward process, and it has many alternative scenarios. Authors should describe in details their model for detonation onset: do they assume that detonation wave lives the ignition tube and travels in the chamber, or do they have an assumption that the detonation wave onset takes place somewhere in the beginning along the whole surface of the chamber cross-section...?”

Authors reply:

“The detonation driver has already been applied to shock tunnels successfully and its detonation onset has been described in many references related to detonation shock tunnels. Instead, detonation is just used a driver in our facility and we do not focus on its combustible processes. We add expiations in the revised manuscript and hope the discussion is sufficient enough to meet the requirements of the reviewer.

“The mixture in the ignition tube is initially ignited by electrical sparks. A high-temperature jet is formed and propagating into the driving section, thereby igniting the detonable gas directly. This will lead to a stable detonation wave traveling downstream in the detonation tube, behind which a Taylor wave follows and the products are at high temperature and pressure.”

Reviewer comment:

The introduced paragraph is misleading the readers. Jet injection leads to a complex transition process, and stable detonation wave can originate at distances surpassing the length of the detonation section of the tube. The structure with plane detonation wave followed by a Taylor wave is a serious approximation, which should be justified by some estimates.

3. Reviewer’s remark: “The paper relying heavily on experimental studies is expected to provide detailed description of the precision of obtained results. The sufficient data should be provided on the errors of measurements, data processing, etc. The experimentally obtained values depicted in figures 5 and 7 should have bars in both directions indicating the possible deviation of measured parameter value.”

Authors’ reply: “We think that we need lots of experimental results to show the exact error bars for the measured parameter value…”

Reviewer comment:

The Authors statement is wrong! There is no need to have many experiments. It is necessary to know the error of measuring equipment, the error of recalculating data, etc. The methods for optional experimental error evaluation are well known, precision of measurements and optional errors are provided along with all measuring equipment. Authors need just to perform estimates.

Authors’ reply:

“However, the facility was newly built and the present numerical method was developed to model the results or explain the dynamic processes within the tube. We also tried to develop this simple method for the identification and assessment of new operating parameters of the test conditions without risk to the facility and hardware, as well as for the validation of new design concepts. We thought that the present work is okay to achieve this goal since the piston/projectile velocities and pressure distributions agreed well with the experimental ones...”

Reviewer comment:

The above paragraph has no relevance to the simple question of experimental measurements error. The error depends not on the new or old facility, but on the measuring devices and data processing.

4. Reviewer’s remark: “Paper relying on data of numerical simulations should provide data on numerical error accumulation. The data on grid convergence study and experimental validation is not sufficient for reliable use of numerical predictions.”

Authors’ reply:

“Our numerical method was first developed in our previous paper (Ref. 23) using Euler equations. And the code was already validated through a high pressure or detonation one-stage gas gun. In the present study, viscous term was added for improvement. And it showed good agreement. Besides, shock tunnel driven detonation was developed and used in our institute for many years and the code for shock tunnels has been developed and validated for many cases.”

Reviewer comment:

Authors reply is irrelevant. Authors state that the code was validated. Validation and verification have nothing to do with numerical error accumulation. It is a great pity, Authors failed to understand that. The model (explicit dynamic codes) can be well validated, and the grid independence proved, nevertheless, accumulation of errors takes place at each integration step due to final size of a cell. The solution converges to the exact for cell size tending to zero. However, for final cell size the error itself depends on accuracy of algorithm and grid, and on the number of integration steps. Thus using the same code, but different number of integration steps in the algorithm, it is possible obtaining either reliable or unreliable results by the end of computations.  The method for accumulation of errors estimations being the function of time steps is described in literature. Authors need just to use the existing formula substituting there data on their code performance for solving particular problem.

 

Conclusion.

Summarizing the above, the Reviewer understood that Authors did not have intention improving the manuscript. Instead, they preferred providing some ill-grounded arguments. The paper cannot be recommended for publication.

Author Response

 

Although we have different opinions about this manuscript, I still need to thank you for review this manuscript. However, I do believe that this manuscript deserve publication since we displayed the detailed experimental or numerical processes clearly. We also developed this simple numerical method for the identification and assessment of new operating parameters of the test conditions without risk to the facility and hardware, as well as for the validation of new design concepts. We achieve this goal since the piston/projectile velocities and pressure distributions agreed well with the experimental ones.

 

In any case, thanks for reviewing this manuscript.

Reviewer 3 Report

Dear Authors,

Thank you for agreeing my remarks and satisfactory answers. I have just several remarks:

1) The "molar" should be added in every table where mixing ratio is applied;

2) In line 265 "ε_θ = 0" should be removed (its value is different from 0 as is shown later);

3) In Table  - units for relative error should be inserted on the left column (to be consistent with another lines/data);

4) let's have a look at the strain-stress relationships (eq. 10-11), we can obtain (after several manipulations), that for ε_θ ≠ 0 and approximately equal to ε_r (as shown in eq. 12 and 13), we can obtain the following relation for σ_r :

see attached .pdf file

 

So the relation for σ_r should be changed and the results should be improved.

This modification should increase the value of σ_r  and probably make the CFD results closer to the experimental data.

If there is a mistake in my suggestion - not to hesitate to argue with me.

Kind regards

Comments for author File: Comments.pdf

Author Response

Dear Editor and Reviewers:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Performance and modeling of a two-stage light gas gun driven by gaseous detonation” (Manuscript ID: applsci-818757). Those comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and have made correction which we hope meet with approval. The corrections are highlighted in the file “Marked manuscript”, and the responds to the reviewer’s comments are as flowing:

 

1) The "molar" should be added in every table where mixing ratio is applied;

The “molar” has been added in each table necessary in the revised manuscript.

 

2) In line 265 "ε_θ = 0" should be removed (its value is different from 0 as is shown later);

"ε_θ = 0" should be removed and it has been corrected in the revised manuscript.

 

3) In Table - units for relative error should be inserted on the left column (to be consistent with another lines/data);

Thanks for your pointing this out. The format has been corrected in the revised manuscript.

 

4) let's have a look at the strain-stress relationships (eq. 10-11), we can obtain (after several manipulations), that for ε_θ ≠ 0 and approximately equal to ε_r (as shown in eq. 12 and 13), we can obtain the following relation for σ_r :

 

You are right about relation for σ_r and we also have the same conclusions about that. There was a typo in Eq. 14 in the last revision and it has been corrected in the revised manuscript.

The authors are really thankful for your valuable suggestions about this manuscript. This facility was newly built and we will continue our work in this two-stage gas gun driven by detonation. We hope that we can make further discussions in the further about our facility.

I am the corresponding author about this manuscript. If you like, we can make further discussions and my email is [email protected]

Author Response File: Author Response.docx