Detonation Transition Research Articles

Deflagration and detonation induced by shock wave focusing at different Mach numbers

Shock wave focusing is an effective way to create a hot spot or a high-pressure and high-temperature region at a certain place, showing its unique usage in detonation initiation, which is beneficial for the development of detonation-based engines. The flame propagation behavior after the autoignition induced by shock wave focusing is crucial to the formation and self-sustaining of the detonation wave. In this study, wedge reflectors with two different angles (60° and 90°) and a planar reflector are employed, and the Mach number of incident shock waves ranging from 2.0 to 2.8 is utilized to trigger different flame propagation modes. Dynamic pressure transducers and the high-speed schlieren imaging system are both employed to investigate the shock-shock collision and ignition procedure. The results reveal a total of four flame propagation modes: deflagration, DDT (Deflagration-to-Detonation Transition), unsteady detonation, and direct detonation. The detonation wave formed in the DDT and unsteady detonation mode is only approximately 75%−85% of the Chapman-Jouguet (C-J) speed; meanwhile, the directly induced detonation wave speed is close to the C-J speed. Transverse waves, which are strong evidence for the existence of detonation waves, are discovered in experiments. The usage of wedge reflectors significantly reduces the initial pressure difference ratio needed for direct detonation ignition. We also provide a practical method for differentiating between detonation and deflagration modes, which involves contrasting the speed of the reflected shock wave with the speed of the theoretically nonreactive reflected shock wave. These findings should serve as a reference for the detonation initiation technique in advanced detonation propulsion engines.

Low/intermediate speed impact‐induced ignition and damage of a novel high‐energy solid propellant

AbstractThe damage and ignition response of a novel propellant is investigated using a modified split Hopkinson pressure bar (SHPB). The mechanical response of the propellant exhibits strong strain rate dependency following a power law. The whole process from mechanical damage to onset of ignition, deflagration and potential deflagration to detonation transition (DDT) under different strain rates (1000–5000 s−1) is captured via high‐speed photography and digital image correlation (DIC). To clarify the onset and extent of the resulting reaction in terms of the mechanical damage caused by impact, meso‐scale analysis is used to evaluate the propellant before and after dynamic impact loading. The ignition response under impact loading is mainly caused by shear flow, and ignition after multiple impacts due to the reflection of stress waves. Dense debris clouds produced by the first impact are observed in the case of a strain rate of 5000 s−1 leading to DDT when the second impact initiated ignition.

Experimental research of the performance and pressure gain in continuous detonation engines with aerospike nozzles

Several continuous detonation engines (CDEs) with aerospike nozzles were designed, and nearly 100 effective experimental tests with methane/GOX were carried out. All tests exhausted to sea level backpressure and were conducted using a calibrated thrust stand and Coriolis mass flow meters. Throughout testing, three key parameters (area ratio, equivalence ratio, and mass flux) affecting CDE operability are discussed in detail. Three normalized parameters were proposed and analyzed to evaluate the performance of CDEs, called the normalized characteristic velocity, the normalized thrust coefficient, and the normalized specific impulse. A new evaluation method for total pressure gain is proposed and implemented. The experimental results showed that lower area ratio (less than 20%) and lower mass flux contribute to form a stable detonation and enjoys a wider range of equivalence ratio. The studied CDEs presented higher performance in the range of area ratio 12.8% - 18.8% and equivalence ratio 1.0 - 1.2. The pressure gain of detonation mode ranged between 15% and 25%, and decreased slightly with the increase of equivalence ratio (0.7 - 1.2). A suitable area ratio is necessary to improve the pressure gain.

Effect of wall roughness on flame acceleration and deflagration-to-detonation transition in a narrow channel

Numerical simulations are conducted to investigate the effect of wall roughness on flame acceleration (FA), deflagration-to-detonation transition (DDT), and detonation propagation in a narrow channel filled with stoichiometric hydrogen-air mixture. The wall roughness is determined by the element height h relative to the pipe diameter d and can be described using a dimensionless number Ra = 2h/d. A high-order numerical algorithm is employed to solve the Navier–Stokes equations on an adaptive mesh. The results show that the roughness enhances the effect of boundary layer and promotes FA and DDT. In channels with small roughness (Ra<0.1), detonation is not observed. Flame instabilities are caused by the interaction between the flame surfaces and reflected waves from the sidewalls, wrinkling of the flame front, leading to additional flame acceleration, and the production of intense pressure waves. In comparison, in channels with large roughness (Ra>0.1), vortices, shears, and even turbulence are produced in the cavity-like regions as leading shock passes over the elements. The mechanisms of the final detonation transition in the rough narrow channel are thought to be the formation of local hot spots arising from the multiple interactions of shocks with the roughness elements and viscous heating of unburned gas in the highly turbulent boundary layer.

Experimental investigation of ethylene-fueled ramjet rotating detonation engine with an annular combustor

A ramjet-mode rotating detonation engine fueled by ethylene is designed to demonstrate the feasibility of rotating detonation organization in annular combustor under high-speed incoming flow condition. The incoming flow with the design total temperature of 860 K and Mach number of 2 at the isolator inlet is provided by an air-heater, and the total mass flow is about 1.0 kg/s. The results show that the ramjet rotating detonation engine can operate in detonation mode when the equivalence ratio (ER) is no less than 0.54. By high-frequency pressure analysis and optical observation, two propagation modes of detonation wave are observed: rotating detonation in the ER range of 0.54-0.71 and longitudinally pulsating detonation in the ER range of 0.82-0.97. In rotating detonation mode, the wave velocity increases as ER increases, and the detonation velocities are about 60% of the CJ value. In longitudinally pulsating detonation mode, the propagation frequencies of the detonation wave are in the range of 1010 Hz-1017 Hz, which is much lower than that in rotating detonation mode, and the upstream propagation velocity of the detonation wave is estimated as 964 m/s. In addition, the maximum static pressure in the combustor increases with the ER from 0.54 to 0.97, and reaches 0.24 MPa when ER is 0.97. When ER is no more than 0.58, the isolator can effectively suppress the back pressure in the combustor, while ER is no less than 0.71, the back pressure in the combustor affects the flow at the isolator inlet, which implies that the isolator design needs to be optimized.

Deflagration to Detonation Transition in Heterogeneous Mixtures Containing Ethanol/Acetone and Oxygen

Liquid fuel is the choice for volume-limited propulsion systems, including detonation-based propulsion. A liquid fuel with high vapor pressure has the advantage of more fuel vapor in the mixture, which supports the transition from deflagration to detonation. This paper reports on an experimental study of deflagration-to-detonation transition (DDT) in a pulse detonation engine with heterogenous mixtures of oxygen and ethanol or acetone. Single-cycle tests were taken for different fuels, equivalence ratios, and DDT enhancement methods. The size distribution of fuel droplets was characterized at the atomizer and engine exit. The effect of the fuel evaporation was dominant for the acetone spray only. Comparing the measured detonation velocities of the two mixtures, a lower velocity deficit relative to the theoretical Chapman–Jouguet detonation velocity was measured for the acetone–oxygen mixtures, and this behavior is related to the higher amount of fuel vapor that existed in the mixtures. Moreover, a shorter transition to detonation was observed in the acetone–oxygen mixture. The addition of a Shchelkin spiral reduced the DDT distance; however, the Chapman–Jouguet condition could be reached only downstream of the obstacle. The measured detonation cell size of the heterogeneous acetone–oxygen mixture was smaller than that of the ethanol–oxygen mixture, indicating that it is more detonable.

Impact of nozzles on the wall-temperature in a valveless pulse detonation engine

As the increase of wall-temperature during the long-duration operation, pre-ignition of the fresh mixture in the filling process often occur in the detonation tube, resulting in the failure of operation. An experimental work has been conducted to investigate the impact of nozzle on the wall-temperature of the detonation tube. In the present study, kerosene and oxygen enriched air were employed in the experiments, and an internally grooved semi-circle spiral, instead of traditional Shchelkin spiral was utilized to facilitate the deflagration to detonation transition (DDT) process. The theoretical results showed that the temperature of fresh mixture increase along the detonation tube during the filling process, and it is likely to be ignited near the open end. It was observed from the experimental results that the convergent section and the divergent section of the exit nozzle has different influence on the wall-temperature. The convergent nozzle will not prevent the wrapping flame near the open end of the detonation tube, and lead to the increase of equilibrium wall-temperature. The nozzle with a diverging section will eliminate the occurrence of wrapping flame during the operation, and the wall temperature near the open end are dramatically decreased. In addition, smaller expansion ratio of the nozzle will lead to lower equilibrium wall-temperature.

Effects of the quantity and arrangement of reactive jet obstacles on flame acceleration and transition to detonation: A numerical study

Solid obstacles induce the detonation in premixed gases while causing significant thrust losses. Jet obstacles can alleviate this deficiency, but there have been few studies on multi-group reactive jet obstacles. In this study, a detailed numerical simulation is performed to investigate the selection of the quantity of reactive jet obstacles and examine the effect of the arrangement of different jet obstacles on flame acceleration and the deflagration to detonation transition (DDT) processes. The results show that there is an optimal quantity of jet obstacles that can rapidly trigger detonation while reducing thrust loss and combustion chamber weight. In terms of flame acceleration, the mechanisms of flame acceleration by reactive jet obstacles with various arrangement types are complex. Specifically, the initial flame acceleration effect of reactive jet obstacles with different arrangement types is similar. However, the staggered arrangement has a longer-lasting vortex structure, stronger leading compression wave and flow field intensity, which provides favorable conditions for the ensuing flame acceleration. When the flame interacts with the jet, the larger virtual blockage ratio and stronger combustion heat release effect further amplify the flame acceleration discrepancy. In DDT, compared with solid obstacles, reactive jet obstacles have more advantages. Different types of jet obstacles arrangement differ in their ability and method in triggering DDT, with the staggered arrangement having the best DDT effect, and detonation initiation modes are divided into two categories: i) the detonation induced by the coupling of the flame surface and the high-pressure region; ii) the reflected wave impinges on the flame surface after the compression waves in front of the flame collide with the wall, resulting in a detonation. Although the quantity and arrangement of jet obstacles vary in this study, all the cases where detonation occurs are consistent with the flame acceleration model of Liberman and similar SWACER mechanism.

Investigation on the explosion dynamics of large-format lithium-ion pouch cells

Explosion is the most extreme case of thermal runaway of lithium-ion (Li-ion) batteries. In this study, explosion dynamics of large-format Li-ion cells are investigated experimentally and numerically. Overcharge-to-explosion tests are conducted on 40 Ah Li-ion cells with Li[Ni0.8Co0.1Mn0.1]O2 cathode. Based on the explosion physics, shockwave and detonation models are used to characterize the shock effect of the cell explosion and evaluate the explosion equivalent. Von Neumann peak is observed on the pressure curves, and the shockwave velocity is supersonic at this time; the unwrinkled spherical flame phenomenon observed in the experiment indicates that it is detonation. Additionally, a geometric model is established based on the real testing scenario, and the explosion behavior is numerically studied. The characteristics of the explosion dynamics process are interpreted and the propagation mechanism of the shockwave are revealed; the deflagration to detonation transition (DDT) phenomenon in this process is caused by the formation of “hot spots”, and the explosion of the cells eventually turns into stable combustion. This study fills the gap in the research on thermal runaway of Li-ion cells, especially in the extreme cases of fire and explosion, and provide useful guidance for battery safety.

Adaptive simulations of flame acceleration and detonation transition in subsonic and supersonic mixtures

Two-dimensional simulations were carried out to investigate the flame acceleration and deflagration-to-detonation transition (DDT) in a combustion chamber filled with a subsonic or supersonic mixture by employing Navier-Stokes equations together with a detailed chemistry reaction mechanism of 11 species and 27 steps under adaptive mesh refinement. The effects of the initial mixture Mach number and mesh resolution on the flame acceleration and DDT were studied in detail, and the entire processes of the flame acceleration, DDT and detonation propagation were revealed. Two DDT mechanisms are obtained in a chamber having the same low blockage ratio but with different initial velocities of the mixture. Regime I: multiple shock wave collisions, shock focusing and shock reflection result in a rapid energy deposition in a small region; a direct detonation subsequently occurs in the boundary wall for the subsonic mixture. Regime II: the classic hot-spot mechanism due to the reactive gradient mechanism is responsible for the detonation transition in the supersonic mixture when the intense leading shock wave impacts and reflects on the solid surface. By increasing the initial mixture Mach number, the run-up time and distance to DDT are dramatically reduced. The flame front structure and propagation in the supersonic flow demonstrate that the detonation cell size rapidly increases when propagating into the smooth region due to detonation attenuation and resulting pressure decrease. Additionally, a much higher combustion temperature occurs in the upper and lower walls because of the Mach stem. In comparison, the results show that the detonation overdrive degree and pressure gain ratio in the subsonic mixture are higher than in the supersonic mixture. Moreover, flame propagation upstream also suggests that increased pressure and temperature occur in the inlet isolation section, even forming a localized explosion point.

Investigating the DDT of H2-Air Mixture in a Rectangular Channel using RANS-Based Numerical Analysis

In this study, a numerical code based on Reynolds-Averaged Navier-Stokes (RANS) method was developed using OpenFOAM to investigate the deflagration to detonation transition (DDT) phenomenon in hydrogen-air mixture gas inside a rectangular channel. The channel was modeled with a thickness of 80 mm and a length of 2000 mm. The numerical simulations were compared with the experimental results and it was found that the developed code qualitatively well simulated the transition process from deflagration to detonation. It was also found that the pressure distribution and reaction progress variables can be useful indicators to understand the instant and location of DDT occurrence. The location of DDT was found to be at the point where the shock wave and the position of the flame front matched. Furthermore, it was observed that the higher the height of the obstacle, the earlier the DDT occurred, but the magnitude of pressure after the DDT did not correlate with the height of the obstacle.

JWST Low-resolution MIRI Spectral Observations of SN 2021aefx: High-density Burning in a Type Ia Supernova

We present a JWST/MIRI low-resolution mid-infrared (MIR) spectroscopic observation of the normal Type Ia supernova (SN Ia) SN 2021aefx at +323 days past rest-frame B-band maximum light. The spectrum ranges from 4 to 14 μm and shows many unique qualities, including a flat-topped [Ar iii] 8.991 μm profile, a strongly tilted [Co iii] 11.888 μm feature, and multiple stable Ni lines. These features provide critical information about the physics of the explosion. The observations are compared to synthetic spectra from detailed non–local thermodynamic equilibrium multidimensional models. The results of the best-fitting model are used to identify the components of the spectral blends and provide a quantitative comparison to the explosion physics. Emission line profiles and the presence of electron capture elements are used to constrain the mass of the exploding white dwarf (WD) and the chemical asymmetries in the ejecta. We show that the observations of SN 2021aefx are consistent with an off-center delayed detonation explosion of a near–Chandrasekhar mass (M Ch) WD at a viewing angle of −30° relative to the point of the deflagration to detonation transition. From the strengths of the stable Ni lines, we determine that there is little to no mixing in the central regions of the ejecta. Based on both the presence of stable Ni and the Ar velocity distributions, we obtain a strict lower limit of 1.2 M ⊙ for the initial WD, implying that most sub-M Ch explosions models are not viable models for SN 2021aefx. The analysis here shows the crucial importance of MIR spectra in distinguishing between explosion scenarios for SNe Ia.

Numerical study on the deflagration to detonation transition promoted by transverse jet

To reveal the mechanism of deflagration to detonation transition promoted by transverse jet, the flame acceleration and detonation initiation process of H2/Air under transverse jet was numerically investigated. According to the flame propagation characteristics and the main factors that promote flame acceleration in different periods, the process of deflagration to detonation transition was divided into four stages: initial flame development stage, turbulence-flame interaction stage, shock-flame interaction stage, detonation initiation stage. The flame acceleration process of each stage was analyzed in detail. The results indicated that the curling and stretching effect of the transverse jet and vortexes on the flame can effectively increase the flame velocity. The flame would constantly produce compression waves during acceleration. The transverse wave formed by the superposition of the compression waves would be reflected multiple times between the walls and act on the flame front, which is critical for flame acceleration. In addition, the positive feedback between the leading shock wave and the flame was also important for the continuous increase of flame velocity.

Experimental research on solid fuel pre-combustion rotating detonation engine

The solid-fuel rotating detonation engine with gas generator is experimentally studied in this paper. This study solved the problems of ignition and stable detonation of pre-combustion gasification injection. The feasibility of solid pre-combustion rotating detonation is verified. A set of gas generators was designed and ignition tests were carried out. The detonation wave velocity is about 2625 m/s in the stable stage, which is about 20% higher than that generated by hydrogen/oxygen detonation. A maximum thrust of 69 N is obtained. Stable detonation pressure signal was obtained in our experiments. It is found that the detonation wave has experienced four stages in the formation process: deflagration, deflagration to detonation transition (DDT) process, galloping detonation, and stable detonation. In the stable detonation stage, coexistence of detonation waves with different strength is identified by high-speed photography images.

Premixed Propane–Air Flame Propagation in a Narrow Channel with Obstacles

Flame interaction with obstacles can affect significantly its behavior due to flame front wrinkling, changes in the flame front surface area, and momentum and heat losses. Experimental and theoretical studies in this area are primarily connected with flame acceleration and deflagration to detonation transition. This work is devoted to studying laminar flames propagating in narrow gaps between closely spaced parallel plates (Hele–Shaw cell) in the presence of internal obstacles separating the rectangular channel in two parts (closed and open to the atmosphere) connected by a small hole. The focus of the research is on the penetration of flames through the hole to the adjacent channel part. Experiments are performed for fuel-rich propane–air mixtures; combustion is initiated by spark ignition near the far end of the closed volume. Additionally, numerical simulations are carried out to demonstrate the details of flame behavior prior to and after penetration into the adjacent space. The results obtained may be applicable to various microcombustors; they are also relevant to fire and explosion safety where flame propagation through leakages may promote fast fire spread.

Effect of fluidic obstacles on flame acceleration and DDT process in a hydrogen-air mixture

Using solid obstacles to accelerate the deflagration to detonation transition (DDT) process induces additional thrust loss, and fluidic obstacles can alleviate this problem to a certain extent. A detailed simulation is conducted to investigate the effects of multiple groups of fluidic obstacles on the flame acceleration and DDT process under different initial velocities and gas types. The results show that, initially, the propagation of reflected shock wave formed by jet impingement is opposite to the flame acceleration direction, thus increasing the initial jet velocity will hinder the flame acceleration. Later, the vortex structure and enhanced turbulence can promote flame acceleration. As the flame accelerates, the virtual blockage ratio of the fluidic obstacles decreases, and increasing initial jet velocity or using reactive jet gases both affect the virtual blockage ratio. Further, increasing initial jet velocity or using reactive jet gases can shorten the detonation initiation time and distance. Compared with solid obstacles, it is concluded that fluidic obstacles can achieve faster detonation initiation with a smaller blockage ratio. Overall, the detonation phenomena in this study are all triggered by hot spots formed by the interaction between reflected waves and distorted flame, but the formation of reflected waves varies.

Numerical investigation of the effect of reactive gas jets on the flame acceleration and DDT process

Jet obstacles can quickly induce the deflagration to detonation transition (DDT) process and reduce the thrust loss of an engine. However, there are few studies on the use of combustible premixed gases as the reactive jet obstacle. Based on the OpenFOAM platform, a detailed numerical investigation of the flame acceleration and DDT process is carried out with different initial jet velocities and the number of jet obstacles. The results show that, although the stronger flame generated by the reactive jet obstacles will reduce the virtual blockage ratio to a greater extent, the turbulence and combustion heat release effect generated by them still significantly promote the flame acceleration. In terms of flame acceleration, initially, increasing the initial jet velocity has no obvious effect on the flame acceleration. Later, turbulence and combustion heat release begin to dominate the flame acceleration and significantly promote the flame acceleration. Since the jets in this study adopt the same combustible premixed gases, increasing the number of reactive jet obstacles downstream does not improve the upstream flame acceleration. In DDT, increasing the initial velocity of the reactive jet can improve the detonation initiation, but the effect of the obstacle number on DDT is greatly affected by the initial jet velocity. Specifically, at a low initial jet velocity, more jet obstacles can significantly promote the detonation initiation, while at a high initial jet velocity, the enhanced turbulence caused by the jet is the dominant factor for the flame acceleration. Therefore, compared with the number of jet obstacles, the detonation initiation process of the premixed gases is more sensitive to the change in the initial jet velocity.

Computational fluid dynamics simulation of detonation wave propagation in modified pulse detonation combustor

In this paper effect of Schelkin spiral material on thermal load and detonation combustion wave propagation in pulse detonation combustor has been simulated. As detonation combustion is supersonic combustion process and energy release rate is very high. In this regards present researches are focusing on flame acceleration process to reduce the DDT run up length. Hence the Schelkin spiral is inserted in detonation tube, which creates a bluff body and enhanced the turbulence of flame propagation. During simulation three turbulence models are used to carry out the reliable and repeatable detonation wave in pulse detonation combustor near thin boundary layer of helical shape Shchelkin spiral. The computational fluid dynamics (CFD) simulation has been performed using Ansys fluent platform. The Large Eddy Simulation (LES), detached eddy simulation with realizable k-ε turbulence model and detached eddy simulation with SST k-ω turbulence model are used for reacting flow simulation. From this simulation the LES turbulence model shows better turbulence initiation of detonation wave with velocity magnitude of 3040 m/s in detonation tube compared to other two turbulence models. This velocity is higher than C-J velocity of 1800 m/s. Further computational result shows that deflagration to detonation transition take place at several waves traveling region, in presence of Shchelkin spiral in detonation tube.

Plasma-assisted deflagration to detonation transition in a microchannel with fast-frame imaging and hybrid fs/ps coherent anti-Stokes Raman scattering measurements

This study examines kinetic enhancement by nanosecond dielectric barrier discharge (ns-DBD) plasma on fuel-lean, Φ = 0.7, dimethyl ether (DME), oxygen (O2), and argon (Ar) premixture during deflagration to detonation transition (DDT) experiments in a microchannel. Nonequilibrium plasma produces active species and radicals as well as fast and slow heating of a mixture to promote ignition due to energetic electrons, ions, and electronic and vibrational excitations. Experiments are conducted to examine the influence of the plasma discharge on the premixture and on the resultant deflagration to detonation transition (DDT) onset time and distance through the use of high-speed imaging and one-dimensional, two-beam, femtosecond/picosecond, coherent anti-Stokes Raman scattering (CARS). A high-speed camera is used to trace the time histories of flame front position and velocity and to identify the dynamics and onset of DDT. The results show that plasma discharge can nonlinearly affect the onset time and distance of DDT. It is shown that a small number of plasma discharge pulses prior to ignition result in reduced DDT onset time and distance by 60% and 40%, respectively, when compared to the results without pre-excitation by ns discharges. The results also show that an increase of number of the plasma discharge pulses results in an extended DDT onset time and distance of 224% and 94%, respectively. Time history of the deflagration wave speed of DME and the analysis of ignition timescale under the choking condition of the burned gas of the deflagration wave suggest low temperature ignition may play a role for DME near the isobaric choking condition of the burned gas and the DDT. Plasma-induced low temperature oxidation of the reactive mixture is assessed via the CO2 to O2 ratio as measured through fs/ps CARS during the gas excitation in discharges. CARS measurements also confirm negligible vibrational and rotational heating of the gas by discharge. The present experiments demonstrate the ability of nonequilibrium plasma to alter the chemistry of DME/O2/Ar premixtures in order to control DDT for applications in advanced propulsion engines.

Studies on the valveless scheme to produce high-frequency detonations with different purge methods

Producing high-frequency detonations is an important topic for pulse detonations which has received considerable attentions. The valveless scheme has been verified to be able to obtain high-frequency detonations more than 100 Hz. This work has been conducted to investigate the possibility to achieve a higher detonation frequency and clarify the limits of stable operations preliminarily for the valveless scheme with different purge methods. Oxygen, ethylene, and nitrogen or liquid water are utilized as oxidizer, fuel, and purge medium in the experiments while two injection configurations are employed. The maximum detonation frequencies of 180 Hz and 330 Hz have been achieved in stable operations for two different injection configurations when nitrogen is used as the purge gas. The ceiling frequency for stable detonations is 300 Hz if nitrogen is replaced by liquid water, which indicates that water vapor is capable to create an efficient buffer zone to ensure stable operations. The results imply that the injection configuration also has a great impact on the ceiling stable detonation frequency. Three operating modes have been observed in this study, i.e., a stable detonation mode, an unstable detonation mode, and a deflagration mode. In the unstable mode, failure of detonation initiation occurs frequently and one interesting phenomenon is that the detonation frequency is reduced by half exactly when insufficient filling happens. The supply pressure ratios of oxidizer to fuel and purge to fuel are obtained for different operating modes when the purge method is changed. Furthermore, the equivalence ratios have been also studied for different operating modes which reveals that the range will change when different purge methods and injection configurations are employed. According to the equivalence ratio and the mass flow rates, an equivalent volume fraction of oxygen is defined and its range for the stable detonation mode is clarified.