Computational Study of Deflagration-to-Detonation Transition in a Semi-Confined Slit Combustor

Round 1

Reviewer 1 Report

The detonation-based engine has performance advantages over the traditional deflagration-based engines due to the pressure gain combustion process. Rotating Detonation Engine (RDE) is one of the detonation-based engine. This paper discusses the conditions for DDT in terms of the minimum height of the combustible mixture layer in the slit, the maximum dilution of the mixture with nitrogen and the maximum slit width. The research results have certain guiding significance for the design of RDE.  However, some issues require further clarification, which are as follows.

1.The ignition energy has an important influence on the DDT process, but the ignition source used in section 2.3 appears to be a linear ignition source and the ignition energy was not given. This is quite different from the ignition method in actual RDE applications. How the conclusion is applicable to RDE? Relevant instructions need to be given in the paper.

2.In a real RDE, the channel is annular, and the bending effect of the wall will affect the initiation process, and the effect of the curved wall is not considered in the simulation of this paper. For curved walls in actual RDE, are the critical heights obtained in this article applicable?

3.The objective of the study is to reveal the conditions for DDT in terms of the minimum height of the combustible mixture layer in the slit, the maximum dilution of the mixture with nitrogen and the maximum slit width. However, it seems only the minimum height of the combustible mixture layer is obtained.  Besides, the minimum height is obtained from the experiment since only the height of 100mm, 50mm and 30 mm are simulated, how about the height of 40mm? It is recommended to add more simulation cases to reveal the maximum dilution of the mixture with nitrogen and the maximum slit width.

Author Response

Thank you very much for the valuable comments. We have made our best to address all the comments in the revised manuscript. Our responses and changes in the manuscript are marked in yellow.

The detonation-based engine has performance advantages over the traditional deflagration-based engines due to the pressure gain combustion process. Rotating Detonation Engine (RDE) is one of the detonation-based engine. This paper discusses the conditions for DDT in terms of the minimum height of the combustible mixture layer in the slit, the maximum dilution of the mixture with nitrogen and the maximum slit width. The research results have certain guiding significance for the design of RDE.  However, some issues require further clarification, which are as follows.

1.The ignition energy has an important influence on the DDT process, but the ignition source used in section 2.3 appears to be a linear ignition source and the ignition energy was not given. This is quite different from the ignition method in actual RDE applications. How the conclusion is applicable to RDE? Relevant instructions need to be given in the paper.

In experiments, the total rated energy E_ign=CU²/2  (C is the capacitance and  U is the voltage), deposited by the spark discharges was approximately 10 J. Taking into account that the actual energy transferred to the combustible mixture can be only 10% [Nettleton, M.A.: Gaseous Detonations, pp. 98–106. Chapman and Hall, London, New York (1987)] of the rated energy, the actual energy deposited by each spark discharge was on the level of 30 mJ, i.e., very small. As for the calculations, it is written at the end of Section 2.3, that ignition is modelled by the spherical expansion of the flame front through the ignition kernel 5 mm in diameter with an apparent velocity U_ign=B*a*u_t . The value of constant B=3 was chosen so that the initial stage of flame propagation in the calculation corresponded well with the experimental observations in a single selected experiment. Further on, this value was fixed. As for the adopted ignition procedure with a linear ignition source, we did not intend here to reproduce the ignition procedure in actual RDEs as it can be different (one or several predetonators; blast caps; electric, laser, and plasma discharges, etc.). The goal was to study the DDT in the semi-confined slit, and the obtained results can be considered applicable both to RDEs and many other applications.

To address this comment, we have added several sentences to Sections 2.1; 2.3; and Conclusions, the new reference [32] to the list of references, and renumbered all subsequent references.

2.In a real RDE, the channel is annular, and the bending effect of the wall will affect the initiation process, and the effect of the curved wall is not considered in the simulation of this paper. For curved walls in actual RDE, are the critical heights obtained in this article applicable?

The wall curvature in the annular RDE could certainly affect the DDT process due to some differences in the flame paths along the shorter “internal” and longer “external” walls of the annular gap and due to shock reflections from “compressive” external and “expansive” internal walls of the gap. These effects complicate the DDT mechanism and depend on the additional factor, that is the wall curvature. As mentioned above, our goal is to study DDT in the semi-confined flat slit rather than in an annular gap typical for RDEs. Nevertheless, to address this comment, we have added the following sentences in Conclusions: “It turns out that for the mild initiation of a detonation, it is necessary to ignite the mixture upon reaching the limiting (minimum) height of the layer of the explosive mixture. For the annular RDEs, this limiting height could additionally depend on the wall curvature.”

3.The objective of the study is to reveal the conditions for DDT in terms of the minimum height of the combustible mixture layer in the slit, the maximum dilution of the mixture with nitrogen and the maximum slit width. However, it seems only the minimum height of the combustible mixture layer is obtained.  Besides, the minimum height is obtained from the experiment since only the height of 100mm, 50mm and 30 mm are simulated, how about the height of 40mm? It is recommended to add more simulation cases to reveal the maximum dilution of the mixture with nitrogen and the maximum slit width.

Actually, we have found the approximate limiting heights of the layer (1) for the stoichiometric ethylene–oxygen mixture with different nitrogen dilution at a fixed slit width (5 mm, see Figure 17) and (2) for the undiluted stoichiometric ethylene–oxygen mixture for three different slit widths (5, 10, and 25 mm, see Figure 20). The comparison with experiment is made only for conditions (1), whereas conditions (2) are currently studied experimentally and will be the subject of future publication. Regarding the intermediate heights of the layer (e.g., 40 mm), it should be understood that the true critical height of the layer cannot be determined with high accuracy for the following reasons. First, as one can see in Figure 9, the layer does not have a clear boundary. Second, at least in experiments, the DDT process is of a stochastic nature: the DDT probability decreases with a decrease in the height of the layer. This was observed experimentally. In view of these circumstances, it looks difficult to obtain the accurate quantitative results for the maximum dilution of the mixture with nitrogen and for the maximum slit width. Note that here we simulate the stage of filling the slit with a combustible mixture rather than use a hypothetical situation in which one simply sets the desired height of the combustible mixture layer with a well-defined boundary as the initial conditions. In view of it, it becomes obvious that there is no point in performing calculations with a step less than 2/3 of the blur layer width, i.e., with a step of ~20 mm (see Figure 9).

Author Response File: Author Response.pdf

Reviewer 2 Report

This study systematically examines the DDT process in a semi-confined channel with the ethylene-oxygen mixture. The major goal is to gain insight into the effects of combustible mixture filling height, nitrogen dilution, and channel width on the DDT process. The results are instructive for the determination of the initiation conditions in the annular RDE combustor. However, there are still some details that need to be improved before the manuscript is published.

1. In Section 2.3, the description of the structure of a single injector is insufficient. Referring to Fig. 3, the cross-sectional size of a single injector is 1×1 mm, is this consistent with the experimental configuration? By the way, the partially enlarged view in Fig. 3 is not clear enough.

2. The dimensioning in Fig. 5 is incomplete and lacks units. Besides, abbreviations of the length units are usually in lowercase rather than uppercase (Fig. 9).

3. The absence of the formation of the exothermic self-ignition center at wider channel widths or nitrogen dilution conditions should be explained.

4. When h_est is 50 mm, the DDT trigger position in the calculation is very different from the experimental result (Fig. 27), and a reasonable explanation should be given for this.

Author Response

Thank you very much for the valuable comments. We have made our best to address all the comments in the revised manuscript. Our responses and changes in the manuscript are marked in green.

This study systematically examines the DDT process in a semi-confined channel with the ethylene-oxygen mixture. The major goal is to gain insight into the effects of combustible mixture filling height, nitrogen dilution, and channel width on the DDT process. The results are instructive for the determination of the initiation conditions in the annular RDE combustor. However, there are still some details that need to be improved before the manuscript is published.

1. In Section 2.3, the description of the structure of a single injector is insufficient. Referring to Fig. 3, the cross-sectional size of a single injector is 1×1 mm, is this consistent with the experimental configuration? By the way, the partially enlarged view in Fig. 3 is not clear enough.

The geometry of the computational domain repeats the experimental one as much as possible. The cross-sectional area of the injector holes and the pitch between them correspond to the experimental setup. The only difference is that the holes are squares rather than circles in the calculations. In general, this should not significantly affect the results of calculations since the geometry of injector holes mainly affects the formation of a blurry layer at the contact boundary of the combustible mixture. To address this comment, we have added an explosive view of injectors in Figure 3.

2. The dimensioning in Fig. 5 is incomplete and lacks units. Besides, abbreviations of the length units are usually in lowercase rather than uppercase (Fig. 9).

We have modified this figure, thank you.

3. The absence of the formation of the exothermic self-ignition center at wider channel widths or nitrogen dilution conditions should be explained.

The deterioration of the conditions for DDT in a more nitrogen diluted mixture is associated with the decrease in mixture reactivity and exothermicity causing slower flame propagation and acceleration. This is explained in Conclusions (item 5). The deterioration of the conditions for DDT in a wider slit is mainly associated with a longer delay of flame arrival to the side walls of the slit also causing slower flame propagation and acceleration. As shown in Figure 24, the flame propagates faster along the side walls of the slit forming a recess on the flame surface in the central part of the slit. To address this comment, we have added the following sentence to Section 3.2.6 and to the Conclusions (item 6):

“The deterioration of the conditions for DDT in a wider slit is mainly associated with a longer delay of flame arrival to the side walls of the slit causing slower flame propagation and acceleration.”

4. When h_estis 50 mm, the DDT trigger position in the calculation is very different from the experimental result (Fig. 27), and a reasonable explanation should be given for this.

The last sentence in the text related to Figure 27 reads: “It should be emphasized that the positions of DDT site in experiments [31] exhibited a rather large scatter.” The latter means that the DDT occurs at different sites of the slit even at careful replication of experimental conditions. It is caused by the sensitivity of the DDT process to many factors including those arising in the course of flame ignition and propagation. This sensitivity increases at approaching the critical conditions like in many other problems of chemical physics. Thus, at the near-critical height of the layer, the scatter appears to be very large and has a “go”–“no go” nature. With increasing the height of the layer above the critical value, the scatter decreases but remains nonzero. By other words, the critical height of the layer is a stochastic variable with a certain mathematical expectation rather than a fixed deterministic value. Therefore, the claim that the critical height of the layer is close to 50 mm means that that the probability of DDT with such a layer is becoming significantly less than 100%. In such circumstances, there is no reason to have a good quantitative agreement between calculated and measured DDT run-up distances and times since we compare the calculation with one particular experiment reported in [31]. We have added this explanation to the text related to Figure 27.

Author Response File: Author Response.pdf

Reviewer 3 Report

This paper developed a CFD model and investigated the effects of several parameters based on the model. The research work is significant and high quality. There's only one problem about the software in this paper. Please indicate the software tools of CFD model. If it is based on commercial software, please delete those equations which is not programmed by authors. If it is open source software, please also mention which sub-model is developed by yourself. 

Author Response

Thank you very much for the valuable comment. We have made our best to address this comment in the revised manuscript. Our response and changes in the manuscript are marked in blue.

This paper developed a CFD model and investigated the effects of several parameters based on the model. The research work is significant and high quality. There's only one problem about the software in this paper. Please indicate the software tools of CFD model. If it is based on commercial software, please delete those equations which is not programmed by authors. If it is open source software, please also mention which sub-model is developed by yourself. 

We used a code of our own development using the open access solvers of linear algebraic equations and stiff equations of chemical kinetics. To address this comment, we have extended the first sentence in Section 2.3:

“The flow equations are solved numerically using a combined Finite Volume – Monte Carlo algorithm realized in the in-house gas dynamic code coupled with the open access solvers of linear algebraic equations and stiff equations of chemical kinetics.”

Author Response File: Author Response.pdf