Numerical Study of the Induction Length Effect on Oblique Detonation Waves

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript titled “Numerical Study of the Induction Length Effect on Oblique Detonation Waves” reveals novel results of how induction length can govern the transition pattern of oblique detonation waves and how it can stabilize or destabilize them. A numerical study was conducted using a two-step induction-reaction kinetic model. The models of this type simulate the reaction process in two stages: the ignition delay (or induction period) stage (characterized by time τi) and the energy release stage (characterized by time τe). It is important to note that the problem of detonation wave stability and its structure cannot be fully addressed based solely on data on ignition delay, without knowledge of the fundamental characteristics of heat release kinetics in general. The need to consider the heat release time in the detonation wave has been highlighted in [1], where a two-step kinetic model was proposed for the first time that accounts for the final rate of chemical reactions at the end of the induction period. Furthermore, in the cited reference, it was pointed out that for the modified model adopted with the forward and backward reactions, the role of the backward reaction, which has usually been neglected in the description of gas parameters behind detonation wave, becomes significant. In the model presented, only the forward reaction has been used to describe heat release.

The effective activation energy during the induction period for hydrocarbon/air mixtures has typical values in the range of 125 to 350 kJ/mol. The effective activation energy associated with the time τe is considerably lower than that for the induction period, τi, and is in the order of 25 kJ/mol [2]. Based on these values, the selection of the E_I and E_R values in this study appears to be quite reasonable. For stationary flow conditions or detonation waves of known velocity, characteristic time can be recalculated to characteristic lengths. The study examined four induction lengths, Li, of 0.01, 0.37, 1.15 and 2.3 mm, with a fixed reaction length, Lr, of 0.66 mm, resulting in a series of ratios Li/Lr of 0.015, 0.56, 1.74, and 3.48. The critical conditions for detonation propagation occur when the induction period, with its high sensitivity to temperature, becomes crucial. The time τi or length Li can be affected by the addition of various promotional or inhibiting additives to the fuel, whereas the value of the time τe or length Lr should remain relatively unchanged [2]. Under the condition that τe is much greater than τi, heat losses are not likely to significantly reduce the energy release zone. In such a case, the kinetics of reaction behind the leading shock wave front are determined by τe (Lr) rather than by τi (Li). This implies that a degenerative explosion with a lower temperature sensitivity of the heat release profile takes place than in a normal explosion. As a result, the detonation wave becomes more stable against gas-dynamic perturbations. This conception is further substantiated in [2]. A similar trend is observed in the numerical simulations presented in this study.

Overall, the manuscript is of high quality and well-written, thus it is recommended for publication after minor revision.

 

The following issues regarding the content require attention:

 

1. It would be helpful to include an additional figure that shows a schematic of the computational domain.
2. It is necessary to specify the wedge angle.
3. Only the dimensionless heat release (Q1 = 20) has been specified. Please specify the value used to convert the heat release into a dimensionless quantity?
4. What is T_S and what is it equal to?
5. Line 86-87: The text in brackets "corresponding to a CJ detonation" has an obscure meaning. Does this have any relation to Li or Lr? What exact value of Li corresponds to a CJ detonation?
6. Line 91-94: There are reasonable doubts about whether the induction length of 0.01 mm could be adequately resolved on a coarse grid with a resolution of 0.025 mm. This implies that you are not resolving the actual induction zone and instead replacing it with a rough and higher calculated value. It should be noted that, in the referenced source, i.e. Ref.[19], in order to ensure a high resolution of the internal structure of the detonation wave, a high and fixed resolution of 128 points per induction zone length has been used. What is the minimum value of Li that would affect the numerical solution in your case? Is there a significant difference in the calculations when Li is set to 0.01, 0.025, 0.05, or 0.1 mm? What is the minimum value of Li, at which the instability of an ODW is suppressed? According to the reasoning in [2], this should occur when Li becomes greater than Lr. The phrase “it is believed that the grid resolution used is enough for the 0.01 mm case” does not instill confidence and seems counterintuitive.
7. It is well-known that the time τi depends on pressure. For example, experiments performed with propane-air mixtures give the dependence τi ~ P^(-0.7), whereas time τe exhibits a much weaker dependence on pressure τe ~ P^(-0.3) [2]. Do you think this change in reaction kinetics could affect the hysteresis phenomenon of oblique detonation in any way?
8. Several language issues have been identified. For example, multiple choice in the phrase “numerically investigated numerically explored” in line 33. In line 86, check the punctuation.

 

References

[1] Korobeinikov, V.P., Levin, V.A. Strong explosion in a combustible gas mixture. Fluid Dyn 4, 30–32 (1969). https://doi.org/10.1007/BF01032469

[2] Borisov A. A. et al. "Heat Evolution Kinetics in High-Temperature Ignition of Hydrocarbon Air or Oxygen Mixtures," Dynamics of Explosions. Progress in Astronautics and Aeronautics. 1988. V.114. P. 124-139. https://doi.org/10.2514/5.9781600865886.0124.0139

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Paper considers oblique detonation waves in supersonic flow. There are a lot publications about this topic, but statement of a paper looks promising. But paper has has a number of disadvantages and can not be recommended to publication.

(1) Introduction must be extended

(2) Numerical methods must be adequately described

(3) Authors must prove that Euler equations and 2D approach can be used for this task

(4) Authors must provide more information about used kinetics and mixture analogues

(5) Conclusions very short and do not provide significant scientific information

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Authors,

The reviewer commends the work presented in the submission draft and believes it has the potential to make a valuable contribution to the field, provided certain issues are addressed. However, several aspects require significant improvement to strengthen the scientific rigor of the results and ensure the manuscript is clear and suitable for publication. The review of the approach and results cannot be performed considering the insufficient information shared in the current document. Kindly consider the following suggestions and address the concerns outlined below:

1. Poor writing: The document suffers from very poor writing style that often is confusing and doesn’t very clearly convey the meaning. For example, consider this line from the introduction (page 1, line 37); “Verreault and Higgins [8] found that ODWs can be prompt with no ignition delay if the leading shock wave is sufficiently strong, and combustion instabilities as well as shock-induced combustion with decoupled shock wave and flame front are also observed under different initial gas pressures or cone angles.” – What does this line convey? Its clear multiple points have been wrapped into one sentence, at the expense of clarity.

The whole document needs rewriting. Specific instances of confusing, poor writing are too many to point out.  The introduction largely owing to the writing is inadequate. It fails to present motivation, the context within which this work is and the importance of current work.

2. Lack of clear scientific discussion on why reaction onset may be delayed or contiguous to the shock front. Better literature review showcasing conditions when there is a transitional behavior would place the current work better. Essentially answering the question,”What does this work answer?”
3. The Experimental Section requires clear details. The purpose of documenting the experimental approach is to validate results, if necessary, by replicating the experiments. It also helps assess the effectiveness of the simulations and validate the assumptions used to replicate real-world conditions, which are particularly important. However, the document barely describes the steps taken. What are the mass and energy conserving equations? What are the assumptions on boundary conditions? What is the reaction mechanism chosen? How is the shock induced into the system? How are the stiffness of equations handled? What is the dimensions of the domain modelled? How does the model converge? Please provide equations and tabulate the constants and terms employed. Please rewrite the experimental section. Providing references [15-17] for the general idea of simulation choices isn’t sufficient.

Comments on the Quality of English Language

Please refer to the comments and suggestions to authors. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

All is well. The authors have provided a detailed response to my comments.

Reviewer 2 Report

Comments and Suggestions for Authors

Comments of my review were not corrected properly. For example: introduction did not cover state of the problem and deep literature review, kinetics were not properly presented with numerical Arrehnius parameters and kinetics tests were not provided...

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for the changes