Steady Detonation Research Articles

Effect of ozone addition and ozonolysis reaction on the detonation properties of C2H4/O2/Ar mixtures

Ozone is one of the strongest oxidizers and can be used to enhance detonation. Detonation enhancement by ozone addition is usually attributed to the ozone decomposition reaction which produces reactive atomic oxygen and thereby accelerates the chain branching reaction. Recently, ozonolysis reaction has been found to be another mechanism to enhance combustion for unsaturated hydrocarbons at low temperatures. In this study, the effects of ozone addition and ozonolysis reaction on steady detonation structure and transient detonation initiation and propagation processes in C2H4/O2/O3/Ar mixtures are examined through simulations considering detailed chemistry. Specifically, the homogeneous ignition process, the ZND detonation structure, the transient direct detonation initiation, and pulsating instability of one-dimensional detonation propagation are investigated. It is found that the homogenous ignition process consists of two stages and the first stage is caused by ozonolysis reactions which consume O3 and produces CH2O as well as H and OH radicals. The ozonolysis reaction and ozone decomposition reaction can both reduce the induction length though they have little influence on the Chapman–Jouguet (CJ) detonation speed. The supercritical, critical and subcritical regimes for direct detonation initiation are identified by continuously decreasing the initiation energy or changing the amount of ozone addition. It is found that direct detonation initiation becomes easier at larger amount of ozone addition and/or larger reaction progress variable. This is interpreted based on the change of the induction length of the ZND detonation structure. Furthermore, it is demonstrated that the ozonolysis reaction can reduce pulsating instability and make the one-dimensional detonation propagation more stable. This is mainly due to the reduction in activation energy caused by ozone addition and/or ozonolysis reaction. This work shows that both ozone decomposition reaction and ozonolysis reaction can enhance detonation for unsaturated hydrocarbon fuels.

Real gas effect on steady planar detonation and uncertainty quantification

The steady planar detonation in hydrogen/air mixture was simulated at elevated pressure. The real gas effect was incorporated by considering the Peng-Robinson equation of state (EoS), nonideal thermodynamic functions and reaction kinetic laws. The nonideal EoS and corresponding thermodynamic functions increase the Chapman-Jouguet (CJ) velocity but decrease the post-shock temperature compared to the ideal gas model, which induces a change of the induction time and distance. The effect of the nonideal reaction rate law depends on the amplitude of compressibility factor and fugacity coefficient and tends to shorten both the induction time and induction distance. These effects counterbalance each other in the complete real gas model which lead to induction time and distance close to the ideal model results. The total heat release was also found to be reduced for the complete model, but the key reactions and their relative importance remain the same as when using the ideal gas model. The nonideal portion of heat release is minor compared with its ideal portion as temperature increases and pressure drops in the reaction zone. The uncertainty of the real gas model, originating from the uncertainty of the parameters in the EoS, was quantified using a Monte Carlo sampling approach. The uncertainty increases linearly with initial pressure and is mainly determined by the species with higher uncertainty factor, larger mole fraction weighted molecular attraction and covolume parameters. Compared to the uncertainty caused by the chemical reaction model, real gas model uncertainty is negligible at low pressure, but becomes of the same order of magnitude at elevated pressure.

Analytical study on detonation pressure and velocity deficit

Steady detonation is studied analytically from the viewpoints of conservation laws and entropy change. The mechanisms affecting the pressure at the end of the rarefaction wave and the velocity deficit are examined. Mass, energy, and momentum conservation are applied in the one-dimensional flow based on the Zeldovich–von Neumann–Doering model. The impulse function is found to be larger at the end of the rarefaction wave than in the region from the detonation front to the Chapman–Jouguet (CJ) sonic point. The extra force propels the detonation gas and is consumed by friction under the moving gas. The friction works in the boundary layer, which changes from laminar to turbulent. The detonated gas expands isentropically from the CJ point to the end of the rarefaction wave. The two-position heat release reaction and friction affect the entropy change during the expansion process. The calculated pressure at the end of the rarefaction wave is in reasonable agreement with past experimental results. The velocity deficits reach several percent and are also in reasonable agreement with previous experiments.

Discrete Boltzmann modeling of detonation: Based on the Shakhov model

A Discrete Boltzmann Model(DBM) based on the Shakhov model for detonation is proposed. Compared with the DBM based on the Bhatnagar–Gross–Krook (BGK) model, the current model has a flexible Prandtl numbers and consequently can be applied to a much wider range of detonation phenomena. Besides the Hydrodynamic Non-Equilibrium (HNE) behaviors usually investigated by the Navier–Stokes model, the most relevant Thermodynamic Non-Equilibrium (TNE) effects can be probed by the current model. The model is validated by some well-known benchmarks, and some steady and unsteady detonation processes are investigated. As for the von Neumann peak relative to the wave front, it is found that (i) (within the range of numerical experiments) the peak heights of pressure, density, and flow velocity increase exponentially with the Prandtl number, the maximum stress increases parabolically with the Prandtl number, and the maximum heat flux decreases exponentially with the Prandtl number and (ii) the peak heights of pressure, density, temperature and flow velocity, and the maximum stress within the peak are parabolically increase with the Mach number, the maximum heat flux decreases exponentially with the Mach number.

Applications of chemical kinetics to detonation: Wave coalescence and homogeneous initiation in single crystal 1,3-propanediol-2,2-bis[(nitrooxy)methyl]-tetranitrate (PETN)

A thermal ignition model is used in parallel with single crystal solid and product fluid Equations of State (EOSs) from the literature to calculate the time and distance to homogeneous shock initiation in single crystal 1,3-propanediol-2,2-bis[(nitrooxy)methyl]-tetranitrate (PETN). The ignition model is a highly constrained, globalized representation of the temperature and pressure dependent decomposition chemistry of PETN. Initiation in the single crystal proceeds via a homogeneous initiation mechanism where thermal ignition results from a well defined initial shock state (P,V,T). The transition to steady detonation at an observed location (x*, t*) then follows when a superdetonation wave initiated by this thermal ignition overtakes the input shock wave. In the traditional approach, P and V are determined directly from measurements and conservation of mass and momentum, leaving T relatively unconstrained due to the extremely nonlinear dependence of T on P, V in the EOS. We present an iterative algorithm to calculate T and V as a function of P from the time to thermal ignition, superdetonation, and intersection at (x*, t*) observed in each experiment. These states are consistent with the unreacted EOS but allow an independent determination of the energy deposited into heating by the input shock. The calculated states compare favorably with pressures and states of compression observed in the experiment but provide a new and interesting set of temperatures associated with each state. We discuss these fully determined initial shock states in (P, V, T) in the context of PETN thermodynamics, specifically the solid/liquid phase boundary at high temperature and pressure.

Reactive burn model calibration using high-throughput initiation experiments at sub-millimeter length scales

A first-of-its-kind model calibration was performed using Sandia National Laboratories’ high-throughput initiation (HTI) experiment for two types of vapor-deposited explosive films consisting of hexanitrostilbene (HNS) or pentaerythritol tetranitrate (PETN). These films exhibit prompt initiation, and they reach steady detonation at sub-millimeter length scales. Following prior work on HNS, we test the hypothesis of approximating these explosive films as fine-grained homogeneous solids with simple Arrhenius kinetics burn models. The model calibration process is described herein using a single-step as well as a two-step Arrhenius rate law, and it consists of systematic parameter sampling leading to a reduction in the model degrees of freedom. Multiple local minima are observed; results are given for seven different optimized parameter sets. Each model set is further evaluated in a two-dimensional simulation of the critical failure thickness for a sustained detonation. Overall, the two-step Arrhenius kinetics model captures the observed behavior for HNS; however, neither model produces a good fit to the PETN data. We hypothesize that the HTI results for PETN correspond to a heterogeneous response, owing to the smaller reaction zone of PETN compared to HNS (i.e., it does not homogenize the fine-grained hot spots as well). Future work should consider using the ignition and growth model for PETN, as well as other reactive burn models such as xHVRB, AWSD, PiSURF, and CREST.

Observations on Detonation Growth of Lead Azide at Microscale.

Lead azide (LA) is a commonly used primary explosive, the detonation growth of which is difficult to study because it is so sensitive and usually has a small charge size in applications. We used photon Doppler velocimetry (PDV) and calibrated polyvinylidene fluoride (PVDF) gauges to reveal the detonation growth in LA, which was pressed in the confinements with controlled heights. The particle-velocity profiles, output pressure, unsteady detonation velocity, reaction time, and reaction-zone width were obtained and analyzed. Three phases of detonation propagation of LA microcharges are discussed. The volume reactions occur at the beginning of detonation in LA microcharges without forming complete shock profiles. Then the shock front is fast with a slow chemistry reaction zone, which is compressed continuously between the height of 0.8 mm and 2.5 mm. Finally, the steady detonation is built at a height of 2.5 mm. The stable detonation velocity and CJ pressure are 4726 ± 8 m/s and 17.12 ± 0.22 GPa. Additionally, the stable reaction zone time and width are 44 ± 7 ns and 148 ± 11 μm. The detailed detonation process has not previously been quantified in such a small geometry.

A three-dimensional discrete Boltzmann model for steady and unsteady detonation

A discrete Boltzmann model (DBM) for compressible reactive flows, with a two-step reaction scheme is presented. The discrete velocity model is modified using the characteristic points of the platonic solids, which leads to excellent spatial symmetry. In the continuum limit, the reactive Navier-Stokes (NS) equations are recovered. This DBM is validated by classic one-dimensional (1D) Riemann problems and 1D detonation. The numerical results agree well with the analytical solutions. Using this model, we simulate three-dimensional (3D) detonations in a rectangular tube. The characteristic features of the 3D detonation are well captured. Two types of experimentally observed detonation modes, namely rectangular mode and diagonal mode are reproduced by the DBM. It is found that the final structures of the detonation are related to the initial perturbation and the width of the tube. The similarity between the diagonal mode and the rectangular in-phase mode is obtained. The predictions of the DBM are in excellent qualitative agreement with the previous studies. Our simulation results indicate a great potential of the DBM to simulate complex reactive flows.

Modelling non-ideal detonations in commercial explosives

Highly non-ideal explosives usually react expressively below their ideal velocities of detonation. In these cases, dimensional effects and product heterogeneities become important to proper model their respective detonation state. Although Direct Numerical Simulation (DNS) techniques can provide a complete and exact solution for this problem, their actual computation cost are still not practical for industrial applications. In order to minimize these constrains, a simplified two-dimensional steady non-ideal detonation model for cylindrical stick explosives is presented. Based on an ellipsoidal shock shape approach (ESSA), the proposed model combines the quasione-dimensional theory for the axial flow solution with the unconfined sonic post-flow conditions at the edge of the explosive. Once calibrated, the model offers the possibility to predict the non-ideal detonation state for any charge diameter, resulting in a full mapping of the diameter-effect curve of the explosive. In addition, the effect of the inert confiner on the detonation flow is calculated by coupling a mechanistic confinement approach with the ESSA model. Thus, the proposed engineering approach is used to model the main properties of one of the most common ammonium nitrate-based explosive used in mining and quarrying industries, including the complete axial flow solution.

Numerička analiza inicijacije glavnog eksplozivnog punjenja artiljerijskog projektila

The importance of investigation of main explosive charge initiation using booster charge stems directly from the objective to optimize the mass of booster charge needed to ensure steady state detonation of main explosive charge in order to achieve maximum projectile efficiency. Considered configuration consists of two explosives and three metal parts which represent elements of fuze and projectile. The main objective of this paper is to develop a numerical model of initiation of main explosive charge of an insensitive artillery ammunition. Through this research two variants of detonation point location were analyzed, ideal and stochastic one. The effects of the detonation transfer are analyzed using the Jones-Wilkins-Lee and Ignition and Growth equation of state models for explosives, applying the Coupled Eulerian-Lagrangian approach in the Abaqus/Explicit software. Analytical computation is introduced in this paper with a purpose to present P-u interaction between configuration elements and for comparison with results obtained by numerical method. The results of analytical and numerical approach are presented and discussed in detail. It is shown that suggested numerical model enables simulation and optimization of explosive train in fuzes of HE projectiles.

Similarity Deviation of Diameter and Thickness Effects

One way to characterize the similarity of detonations (in the sense of their reaction rate) is through size effect tests. Using cylinders (rods), they’re called diameter effect tests, and using slabs, they’re called thickness effect tests. From the steady state equations of motion of these configurations it follows that they scale as r(D)=h(D), where r=rod radius, h=slab thickness, and D=steady detonation velocity. But tests show deviations from such scaling. Here we propose an explanation to these deviations. The explanation is based on a previous work in which we show that a boundary layer of partial reaction usually forms when a detonation wave is grazing along a free boundary. We suggest and show via computer simulations that those scaling deviations are related to this partially reacted boundary layer effect.

Effect of microstructure on mechanical properties of titanium-steel explosive welding interface

Explosive welding, as a well-known composite processing technology, can be used to weld two or more similar and dissimilar materials. Generally, periodic wavy interfaces are formed in the bonding zone during explosive welding process. The bonding strengths of the welding interfaces are largely influenced by the microstructure of the welding interface. In this paper, the effects of microstructure on mechanical properties of titanium-steel explosive welding interface were presented. The bonding interface with different microstructure at different locations of the titanium-steel welding interface can be characterized as three distinct zones due to different stages of detonation wave propagation including the detonation growth zone near the initiation point, steady detonation zone and reflection-affected zone near the far-end boundary. The microstructure of interfaces was investigated by optical microscopy, scanning electron microscopy, energy dispersive spectrometer. It was found that a nearly straight interface with a small wavy interface was created in the detonation growth zone near the initiation point, and an irregularly wavy interface was formed in the reflection-affected zone near the far-end boundary. While a periodic wavy interface with various defects (e. g. microcracks, voids and intermetallic compounds etc.) was formed in the steady detonation zone. A small-size H-shaped specimen was used to evaluate the tensile properties of interfaces with the bonding interface perpendicular or parallel to the tensile loading direction. The results indicated that the amplitude and wavelength of wavy interfaces showed a tendency of increasing, plateauing and decreasing, corresponding to the detonation growth zone, steady detonation zone and reflection-affected zone, respectively. The mechanical properties of the bonding interface along the detonation direction also displayed a similar tendency. The periodic wavy interface in the steady detonation zone exhibited the highest strength. Notably, the defects, such as microcracks, void and intermetallic compounds in the vortex area had significant effects on the mechanical properties of the bonding interface.

Experimental study on detonation propagation in industrial scale pipelines used in petrochemical plants

Based on the lack of systematic research on flame propagation in large-diameter and long-distance pipelines in the tank area of petrochemical plants, an experimental device for flame propagation in DN50-DN500 industrial-scale pipelines was designed and built. In this paper, effects of concentration of gas mixture for propagation characteristics of steady gaseous detonation waves in ethylene-air mixtures with DN50 pipeline were studied experimentally. The volume concentration of gas mixture was 5.6%, 5.93%, 6.6%, 7.15%, 8.0% ethylene in air. Homogeneous C2H4/air (6.6%) and C3H8/air (4.2%) mixtures were used with 9 kinds of pipelines which were from DN50 to DN500 to study the effects of pipeline diameter for propagation characteristics of steady gaseous detonation. The experimental results show that the concentration of combustible gas has an effect on flame propagation and detonation. The detonation runup distance is short and steady detonation is more likely to be formed when it is close to chemical equivalent concentration, when the combustible mixture is poorer or richer, the steady detonation will need more runup distance. The detonation flame speed and pressure are more affected by the type of combustible gas instead of pipe diameter. The detonation pressure of the mixture of 6.6% C2H4/air and the mixture of 4.2% C3H8/air is 15.17 and 14.47 times of the initial pressure, respectively, which is different from the reference value given by the ISO16852 standard where the ratio pm/p0 (the average value of the detonation pressure to initial pressure) increases with pipe diameter. The detonation pressure of pipeline below DN150 is far higher than the reference value which is 10 and 12. It’s suggested that in the design of pipelines and selection and installation of flame arresters for connecting pipelines in the tank areas, detonation pressure requires careful consideration and appropriate arresters should be selected in combination with the installation position.

Numerical modelling of steady detonations with a variational streamline approach

Previous studies (Watt et al. in J Eng Math 75(1):1, 2012; Cartwright and Falle in J Eng Math 115(1):157, 2019) have shown that a streamline based approach to modelling of steady state detonations can produce good results for rate laws which have maximal reaction at the shock. In this paper we consider a Variational Streamline Approximation (VSA) which introduces streamline curvature. Comparing results with Direct Numerical Simulations (DNS) and the existing Straight Streamline Approximation (SSA) model, we find that the VSA improves the predictive accurary of streamlines modelling compared to DNS calculations, capturing the shock front and sonic surfaces with greater accuracy than SSA.

NUMERICAL INVESTIGATION ON THE SPACE-TIME CORRELATION BETWEEN OBLIQUE DETONATION AND NORMAL DETONATION PROPAGATION

The propagation theory of one-dimensional detonation is complete and accurate, while prediction of two-dimensional oblique detonation propagation with large scale and high accuracy is still difficult primarily due to the treatment of wedge wall during the calculation and the modelling of viscosity. In this paper, the space-time correlation between two-dimensional steady oblique detonation induced by finite wedge and one-dimensional unsteady detonation supported by piston is investigated by numerical simulations of multi-species Euler equations with H2-Air detailed chemical kinetics. The initiation and propagation process of detonation wave, together with its interaction with rarefaction waves are numerically analyzed from the perspective of both space and time. The results show that under the same overdriven degree, the wave structure, wall parameters and profile variation calculated from one-dimensional case fit well both qualitatively and quantitatively with two-dimensional case after a certain space-time transformation, which validates the space-time correlation between one- and two-dimensional detonation waves. The difference mainly lies in the transition process between different stages of detonation development, such as the transition from over-driven oblique detonation wave to near Chapman-Jouguet (CJ) oblique detonation wave under the effect of rarefaction waves. Since most features of oblique detonation waves over finite wedge can be obtained efficiently by one-dimensional numerical calculation of piston-driven detonation and space-time transformation, the present work provides a feasible way to understand the spatial structure of oblique detonations waves, including detonation initiation, formation of over-driven oblique detonation and cellular structure downstream. Besides, this paper also provides a novel method to distinguish the effect of wall compression and boundary layer by comparing one- and two-dimensional numerical results. Moreover, the results imply that two-dimensional flow field over wedges of different shapes can be obtained with satisfying accuracy by altering the velocity of piston, which greatly reduces the time, cost and complexity of numerical simulation during the design of combustion chamber in an oblique detonation wave engine.

Effect of the reactor model on steady detonation modeling

The effect of employing four different reactor models, Zeldovich–von Neumann–Döring (ZND), constant volume (CV), constant pressure (CP), and the Shock routine from Chemkin, to perform detonation-relevant chemical modeling was assessed. The simulation results were compared in terms of characteristic length scales and chemical analyses with four representative mixtures: $$\hbox {H}_{2}{-}\hbox {O}_{2}{-}\hbox {N}_{2}$$ , $$\hbox {H}_{2}{-}\hbox {NO}_{2}/{\hbox {N}_{2}}{\hbox {O}_{4}}$$ , $${\hbox {C}_{3}}{\hbox {H}_{8}}{-}\hbox {O}_{2}{-}\hbox {N}_{2}$$ , and dimethyl ether (DME)– $$\hbox {O}_{2}{-}\hbox {CO}_{2}$$ . The following conclusions were drawn: (i) CV and CP reactor models shorten the induction zone length and strengthen the energy release rate in most mixtures. In terms of chemical kinetics, the impact of CP and CV reactor models is quite limited for $$\hbox {H}_{2}{-}\hbox {O}_{2}{-}\hbox {N}_{2}$$ and $$\hbox {H}_{2}{-}\hbox {NO}_{2}/{\hbox {N}_{2}}{\hbox {O}_{4}}$$ mixtures. However, the C2 branch is enhanced in CV and CP reactor models for $${\hbox {C}_{3}}{\hbox {H}_{8}}{-}\hbox {O}_{2}{-}\hbox {N}_{2}$$ mixture. Moreover, both reactor models weaken the intermediate-temperature chemistry and promote the high-temperature chemistry for DME– $$\hbox {O}_{2}{-}\hbox {CO}_{2}$$ mixtures; (ii) the Shock module can be employed to perform detonation modeling, as it provided similar results to the ZND simulations for all investigated mixtures; and (iii) the ZND reactor model is preferred over the zero-dimensional reactor models, while the Shock module of ANSYS is equivalent to the ZND reactor.

Three-dimensional multiple-relaxation-time discrete Boltzmann model of compressible reactive flows with nonequilibrium effects

Based on the kinetic theory, a three-dimensional multiple-relaxation-time discrete Boltzmann model (DBM) is proposed for nonequilibrium compressible reactive flows where both the Prandtl number and specific heat ratio are freely adjustable. There are 30 kinetic moments of the discrete distribution functions, and an efficient three-dimensional thirty-velocity model is utilized. Through the Chapman–Enskog analysis, the reactive Navier–Stokes equations can be recovered from the DBM. Unlike existing lattice Boltzmann models for reactive flows, the hydrodynamic and thermodynamic fields are fully coupled in the DBM to simulate combustion in subsonic, supersonic, and potentially hypersonic flows. In addition, both hydrodynamic and thermodynamic nonequilibrium effects can be obtained and quantified handily in the evolution of the discrete Boltzmann equation. Several well-known benchmarks are adopted to validate the model, including chemical reactions in the free falling process, thermal Couette flow, one-dimensional steady or unsteady detonation, and a three-dimensional spherical explosion in an enclosed cube. It is shown that the proposed DBM has the capability to simulate both subsonic and supersonic fluid flows with or without chemical reactions.

Shock focusing effects on silica phase production during cyclotrimethylene trinitramine/2,4,6-trinitrotoluene detonations

Detonation is an increasingly studied method for the synthesis of nanomaterials due to the rapid reaction rate producing extreme pressures and temperatures for short durations, which can result in the production of ultra-hard and high-temperature nanomaterials. The present study shows that phase formation in detonation depends on the distribution of inert additives in the explosive charge. Numerical simulations and experimental validation were conducted on silica powders that were shock loaded by detonation of a 3.8 cm diameter cylindrical explosive charge composed of cyclotrimethylene trinitramine, 2,4,6-trinitrotoluene, and paraffin wax. Silica was incorporated into the explosive in three configurations and at two different starting particle sizes in both simulation and experiments. The detonation residues were purified to concentrate the silica and characterized via x-ray diffraction with Rietveld refinement and optical microscopy. Loading conditions and silica phase morphology were not consistent between the configurations and starting size of silica incorporated into the charge. The implication of these results is that the prediction of phase production in detonation synthesis experiments cannot be based on Chapman–Jouguet steady detonation parameters of the explosive matrix but must also include analysis of shock interaction and heat transfer into the additives incorporated into the explosive.

Standing window of oblique detonation with pathological behaviour

Standing of an Oblique Detonation Wave (ODW) on a wedge within combustor is the prerequisite of thrust generation for ODW engine which is regarded as a novel and conceptual propulsion device with hypersonic flight Mach number. Usually a standing window of ODW is defined as the wedge angle ranged from the ODW detached angle from wedge (upper limit) to the angle that a Chapman-Jouguet (CJ) detonation occurs (lower limit). For pathological detonation cases, however, the CJ detonation cannot be achieved, and thus the lower limit of the standing window of ODW should be revisited. In present study, two types of reactions in hypersonic incoming flow that include the behavior of pathological detonation, that is, the single-step irreversible reaction with mole variation and the two-step irreversible reactions with exothermic process followed by endothermic process, have been used for studying standing behavior of ODW. The steady detonation polar analysis of ODW is carried out for both reaction systems. The results reveal that the reaction with more mole decrement and the reactions with stronger endothermic process show the pathological detonation feature and therefore modify the lower limit of standing window of ODW. Three equivalent parameters are proposed to quantitatively measure the standing window range of ODW from points of view of thermodynamics, Mach number of incoming flow and heat effect of reactions. It is found that the standing window of ODW is determined by the specific heat ratio, the overdrive degree of detonation and the endothermic level of the hypersonic incoming flow, regardless of whether the detonation is pathological or not.

An experimental study of detonation propagation and re-initiation for acetylene–air mixtures in a narrow channel

Detonation propagation, re-initiation, and flame propagation in acetylene–air mixtures were investigated in a channel with a transverse dimension that is comparable with the width of the detonation cell. Experiments were carried out in a channel with a square cross-section of 5 mm $$\times $$ 5 mm. The detonation wave passed from the driver section into the transparent test section. The trajectories of the propagation of glowing combustion products (high-speed image sequences) were recorded, and high-speed schlieren image sequences of the reaction zone and shock waves were obtained. The flame front velocity was measured. The intensity of the shock waves was measured with piezoelectric pressure transducers. Depending on the equivalence ratio ER, four modes of combustion propagation were detected: (1) steady detonation; (2) decay and re-initiation of detonation; (3) detonation decay and flame acceleration; and (4) detonation decay and the absence of flame acceleration. Quantitative evaluation of the boundary layer thickness was carried out. The intensity of the shock wave and the flame front velocity were analysed for different modes. It was shown that the re-initiation of detonation in a mixture of acetylene and air with $$\text {ER} = 1.6$$ is characterized by a spatial interval of $$1000\pm 50$$ mm and a time interval of $$1300\pm 100~\upmu \hbox {s}$$ .