Detonation Wave Research Articles

Computational investigation on the formation of liquid-fueled oblique detonation waves

Utilizing a two-phase supersonic chemically reacting flow solver with the Eulerian-Lagrangian method implemented in OpenFOAM, this study computationally investigates the formation of liquid-fueled oblique detonation waves (ODWs) within a pre-injection oblique detonation wave engine operating at an altitude of 30 km and a velocity of Mach 9. The inflow undergoes two-stage 12.5° compression, followed by uniform mixing with randomly distributed n-heptane droplets before entering the combustor. The study examines the effects of droplet breakup models, gas-liquid ratios, and on-wedge strips on the ODW formation. Results indicate that under the pure-droplet condition, the ODW fails to form within the combustor, irrespective of the breakup models used. However, increasing the proportion of n-heptane vapor in the fuel/air mixture facilitates the ODW formation, because the n-heptane vapor rapidly participates in the gaseous reactions, producing heat and accelerating the transition from low- to intermediate-temperature chemistry. Additionally, the presence of on-wedge strips enhances ODW formation by inducing a bow shock wave within the combustor, which significantly increases the temperature, directly triggering intermediate-temperature chemistry and subsequent heat-release reactions, thereby facilitating the formation of ODW.

Numerical research on flow field structure and droplets distribution of kerosene-fueled rotating detonation ramjet engine

In order to reveal the multiphase flow field structure and fuel droplets distribution under rotating detonation ramjet engine fueled by liquid kerosene, non-premixed simulations coupled with an Euler-Lagrangian approach is adopted. Supersonic air is used as oxidizer and the total pressure and total temperature at the entrance of isolation are set as 1.2 MPa and 1100 K, respectively, with a Mach number of 1.9. It is shown that a single-wave is formed and typical rotating detonation wave structures are established under two different orifice spacing conditions, namely 2 mm and 6mm. A "rich oil and poor oxygen band" is formed and attributed to the inconsistent supply of fuel and air after the passage of the detonation wave. When the orifices spacing is increased from 2 mm to 6 mm, both obvious strips after the detonation wave and “n-type” deflagration structures near the contact surface are observed. Besides, the detonation wave front becomes discontinuous, as well as from the deflagration heat release distribution. Despite of the effect of the circumferential propagation of detonation wave, kerosene droplets still propagate mainly along the downstream direction. However, Kerosene droplets distribution shows obvious difference along the detonation wave propagation direction.

Dynamic interaction patterns of oblique detonation waves with boundary layers in hypersonic reactive flows

Due to their high thermal cycle efficiency and compact combustor, oblique detonation engines hold great promise for hypersonic propulsion. Previous numerical simulations of oblique detonation waves have predominantly solved the Euler equations, disregarding the influence of viscosity and boundary layers. This work aims to study how the interaction between the oblique detonation wave and the boundary layer influences the detonation wave structures in confined spaces. Two-dimensional numerical simulations considering detailed chemistry are performed in a stoichiometric H2/air mixture. The results indicate that the wedge-induced oblique detonation wave generates a strong adverse pressure gradient upon impacting the upper wall, leading to boundary layer separation. The separation zone subsequently induces an oblique shock wave near the upper wall, and an increase in separation angle will cause the transition from an oblique shock wave to an oblique detonation wave. The formation of the separation zone reduces the actual flow area and may even lead to flow choking; its obstructive effect is similar to that of the Mach stem in inviscid flow. To establish a connection between the viscous recirculation zone and the inviscid Mach stem, we introduce a dimensionless parameter, η, based on the inviscid assumption. It is defined as the ratio of the inviscid Mach stem height to the channel entrance height. This parameter can be used to identify three wave systems in a viscous flow field: separation shock-dominated wave systems, separation detonation-dominated wave systems, and unstable Mach stem-dominated wave systems. Among these, the appearance of detonation Mach stems leads to flow choking, and the shock-detonation wave system continually moves upstream, ultimately causing the failure of the oblique detonation combustion. The findings of this study provide new insights into the investigation of the influence of viscosity on the flow structure of oblique detonation waves.

The propagation characteristics of a detonation wave in uniformly premixed gases within a semi-confined channel

Based on the OpenFOAM platform, a numerical study was conducted to investigate the propagation characteristics of a detonation wave in uniformly premixed gases within a semi-confined channel, specifically examining the changes in wave's structure and analyzing the detonation reinitiation-extinguishment process. The results indicate that, due to the weak confinement, the detonation wave experiences lateral expansion, with transverse waves on the detonation wave front penetrating into the inert gas and forming segmented protrusions on the oblique shock wave. During the propagation process, the number of transverse waves decreases gradually, and the reflected waves formed by the interaction between transverse waves and the inert gas are weak, collectively leading to a gradual decay in the strength of the detonation wave and a reduction in the frequency of pressure oscillation on the detonation wave front. Furthermore, when transverse waves interact with the inert gas and undergo Mach reflection, the reflected waves would detach the inert gas and form new transverse waves promoted by upward-moving old transverse waves and disturbances on the flame front, thereby extending the duration distance of the detonation wave. Subsequently, after the detonation wave decouples, a transverse wave reflected from the inert gas interface interacts with the lower wall, triggering local detonation reinitiation, which generates a higher-intensity longitudinal wave that couples with the leading shock wave, temporarily restoring the detonation wave and forming lateral detonation in the decoupled region. However, the detonation wave will ultimately extinguish due to the attenuation of transverse waves' intensity and decreasing number of these waves.

Existence condition for detonations in condensed explosives with pressure–temperature equilibrium models

Most engineering tools dealing with detonation waves in condensed explosives are based on the reactive Euler equations, which involve a thermodynamic closure based on temperature and pressure equilibrium conditions. Indeed, the reactant and the detonation products are assumed to evolve in mechanical and thermal equilibrium. Although the assumption of thermal equilibrium is physically questionable, the reactive Euler equations are used for convenience. This choice is supported by several reasons. When considering thermal equilibrium, the assessment of thermal exchanges between the reactant and the detonation products is simplified, as no exchange coefficient needs to be determined. Furthermore, the reactive Euler equations are in conservative form and the shock relations are well-defined. This model appears to be the simplest option for addressing detonations in condensed explosives. However, this simplicity has limitations and conceals a subtle difficulty that can lead to pathological detonations. The present contribution investigates this difficulty and presents a global exothermic condition to preserve exothermic detonations in the frame of temperature–pressure equilibrium flow models. This condition depends on the equations of state only. It is independent of the kinetics used to model the decomposition of the explosive. By meticulously selecting the thermodynamic parameters of the equations of state for the reactant and detonation products, pathological detonations are prevented, thereby maintaining a globally exothermic reaction consistent with the Zeldovich–von Neumann–Döring theory.

Analytical study of rotating detonation and engine operating conditions

In this paper, the mechanism of rotating detonation is analytically discussed using a two-dimensional sheet model. Two ratios are employed in this discussion: the ratio of the sonic point width to the detonation front width, and the ratio of the effective mixture injection area to the injection area. In the rotating detonation, the unconfined boundary can increase the width at the sonic point and decrease the detonation wave speed. Although the high detonation pressure hinders mixture injection, effectively preventing some injectors from functioning, the high pressure acting on the injection end wall produces thrust. Mass, momentum, energy, and angular momentum conservations are used to determine these ratios. The calculated results are in reasonable agreement with past experimental and numerical findings. The present model succeeds to clarify the features, parameter relationships, and overall mechanism of the rotating detonation analytically and to specify flow field of the rotating detonation under given boundary conditions, e.g., the velocity deficit and the effective injection area ratio. The specific impulse of a rotating detonation engine was lower than that of an ordinary rocket engine due to the lower combustion gas pressure when the combustion gas expanded to 1 atm. The thrust coefficient and the specific impulse of an air-breathing rotating detonation engine were shown to be lower than those of a ramjet engine, respectively, primarily because of the smaller airflow rate into the engine.

Effect of pre-shock on the expanding fracture behavior of 1045 steel cylindrical shell under internal explosive loading

Explosively driven expansion fractures in metallic shells will be preceded by a compression shock wave, which inevitably changes the mechanical and microstructural state of the shell materials and thus affects their subsequent dynamic deformation and expansion fracture processes. To understand the influence of pre-shock pressure on the dynamic expansion fracture behavior of metallic shells, the incident shock waves with varying peak pressure were generated in a 1045 steel cylindrical shell by sweeping detonation wave loading. The pre-shock and subsequent expansion fracture processes were continuously diagnosed by combining a high-speed framing camera and the arrayed Photon Doppler Velocimetry (PDV) measurements to obtain the fracture strains at different axial positions (corresponding to different pre-shock pressures). The results clearly show that the pre-shock pressure during detonation loading has a significant effect on the expansion fracture properties of the 1045 steel cylinder; the fracture strain remarkably decreases with the increase of pre-shock pressure from ∼19 GPa to ∼20 GPa and then changes gently in the range of ∼20 GPa to ∼22 GPa. Metallurgical analyses reveal increased densities of microstructural defects, including dislocations and deformation twins, when a shock wave passes through, resulting in a reduced capacity for further defect storage in the shocked metals, ultimately leading to a decrease in the fracture strain during the subsequent expansion deformation process.

Wave mode observation of hydrogen/oxygen driven rotating detonations in the hollow and annular rotating detonation rocket engine

The rotating detonation rocket engine (RDRE) fueled by hydrogen/oxygen propellant represents a promising propulsion technology due to its high thermodynamic efficiency and propellant superior specific impulse. The rotating detonation wave (RDW) must propagate in a specific propagation mode while maintaining the self-sustaining state to ensure stable operation. An experimental system of hydrogen/oxygen fueled RDRE was developed in the present study. The operation of RDRE and propagation mode of RDW were investigated under atmospheric pressure conditions, and both hollow and annular combustors were tested. The high-frequency pressure fluctuations in the RDRE were measured by the dynamic pressure transducer, while a high-speed camera was used to capture images of flame luminescence at the rear end of the RDRE. The experimental results showed that the RDW could be initiated and reached a self-sustaining propagation state with hydrogen/oxygen propellant in the hollow and annular RDRE. A single-wave mode, a two-wave co-rotating mode, and a three-wave co-rotating mode were visualized under different conditions. With the increase in the equivalence ratio, the number of rotating detonation fronts decreased, and the variations in the RDW propagation modes were consistent in the hollow and annular RDRE. However, when the equivalence ratio exceeds 1.2, the propagation velocity decreases sharply in the annular combustor, while in the hollow combustor the RDW propagates stably, revealing a higher upper limit for the equivalence ratio. Also, the dominant frequency distribution was more concentrated in the hollow combustor. The findings provide valuable insight into the variations in detonation modes related to the equivalence ratio and combustor configuration.

Numerical study on flow and combustion properties of oblique detonation engine in a wide speed range

Ensuring safe flight is a fundamental prerequisite for developing hypersonic propulsion systems. A comprehensive investigation of the steady boundary associated with oblique detonation wave in a wide speed range was conducted, with the aim of exploring the feasibility of oblique detonation engine across a diverse array of flight conditions. In this study, the wedge angle applicable in a wide-speed range was acquired via the analysis of oblique detonation wave polar curve. The configuration of the internal injection oblique detonation engine was subsequently designed and established, considering the effect of fuel-air inhomogeneity and complex wave system interactions within a confined combustor. The compressible Euler equations coupled with a 9-species and 19-step chemical reaction mechanism are employed to simulate the oblique detonation process. Ultimately, the safe flight envelope of an air-breathing vehicle equipped with the internal injection oblique detonation engine is mapped across a broad range of Mach numbers, demonstrating the engine’s capability to operate within the Mach 8 to 12 range. Furthermore, the findings reveal that decreasing either the flight Mach number or altitude results in unsteady oblique detonation wave within the internal injection oblique detonation engine combustor, however, reducing the equivalence ratio can stabilize the oblique detonation wave once again. This study provides valuable guidance for the design and wide-speed-range operation of an internal injection oblique detonation engine.

Investigation on the integrated characteristics of n-decane/air rotating detonation combustor and supersonic turbine

In this study, the two-dimensional numerical simulations are conducted to study the flow field characteristics, turbine performance and loss mechanism of integrated system of rotating detonation combustor and supersonic turbine under two different directions of detonation wave propagation. The results indicate that the propagation direction of RDW affects the incident angle between OSW and guide vanes, resulting in different operating modes for aligned and unaligned modes. OSW in the turbine cascade undergoes the leading-edge shock, blade surface reflection and trailing edge diffraction. The backward-propagating rake-type shock envelope is formed due to leading-edge shock of the rotor. In misaligned mode, the stator has higher damping of both pressure and temperature. The stator significantly improves the circumferential uniformity of both velocity and pressure, particularly when operating in aligned mode. The total pressure loss in aligned mode is less, therefore the turbine achieves higher rim work and efficiency. The viscosity is one of the main sources of loss in the flow field. The reflected shock waves at the leading edge of the rotor and in the stator cascade are the primary factors contributing to the leading-edge vortices on the stator vanes.

Study on concentration distribution and detonation characteristics of typical multiphase fuel in orthogonal flow field

The fuel concentration distribution and detonation characteristics are important for performance evaluation. In order to meet the needs of airdrop, launcher and missile, the transient flow and detonation process of multiphase fuel in orthogonal flow field are analyzed by experiments and numerical simulations. The dynamic detonation model of ethyl ether (EE), propylene oxide (PO) and tetrahydro dicyclopentadiene (JP-10) is built. The flow process, concentration distribution, overpressure, temperature and detonation wave structure of the three fuels are obtained. The results show that the falling velocity has obvious influence on the detonation process of fuel droplets. The falling velocity of 0.5 Ma makes the fuel concentration distribution more uniform and the energy output is better. The peak overpressure of EE, PO and JP-10 is 2.88 MPa, 3.21 MPa and 2.96 MPa respectively. The peak temperature is 2885 K, 3230 K and 2955 K respectively. The burn out rate increases by 8.5%, 8.1% and 13.7% respectively. JP-10 has higher sensitivity to falling velocity, and there are obvious secondary peaks of overpressure in low-speed state. PO has higher stability for falling velocity, and the scaled length of high temperature/pressure after detonation wave is 0.145 m·kg-1/3.

Numerical Study of Detonation Waves in Gas Suspensions with Spatially Inhomogeneous Particle Concentration Distribution in Sharply Expanding Pipes

The article presents some results of a numerical study of detonation waves in gas suspensions with a spatially inhomogeneous distribution of particle concentration in sharply expanding pipes obtained by the large particle method. The purpose of the research is to study the influence of pipeline geometry and longitudinally spatially inhomogeneous distribution of particle concentration on the propagation of detonation waves in gas suspensions. It is shown that the size of the narrow and wide parts of the pipeline, as well as, the spatially inhomogeneous distribution of particle concentrations, qualitatively and quantitatively affect this process. Three detonation modes have been identified: continuous wave propagation, complete cessation, and partial disruption with subsequent recovery. It has been established that, at a fixed total mass of suspension, a layer with a linearly decreasing law of change in the concentration of unitary fuel particles better attenuates detonation waves than with a linearly increasing and homogeneous one.

Preparation of spherical DAOAF with micro-nano structure by emulsion method: To improve short-pulse initiation performance

In order to take into account the advantages of good processing performance of micron 3,3′-diamino-4,4′-azoxyfurazan(DAOAF) and high sensitivity of short-pulse initiation of nano DAOAF, Spherical DAOAF products with nano-microstructure were prepared by oil-in-oil emulsion method. The laser-induced air shock wave detonation performance, mechanical sensitivity and short-pulse initiation sensitivity of raw DAOAF and spherical DAOAF were tested and compared. The results showed that the optimum process conditions of emulsion stability were as follows: using Tween-80 as the surfactant at a concentration of 0.3 g·mL−1, a solvent-non-solvent volume ratio of 1:3, and emulsion standing time less than 10 minutes. Compared to the raw DAOAF, the crystal structure of DAOAF sample prepared by emulsion method did not change, only the morphology changed. The DAOAF sample prepared by emulsion method is spherical, and the surface is self-assembled by nanorod-like DAOAF, the particle size distribution is uniform and the dispersion is good. The thermal decomposition peak temperature of spherical DAOAF did not change significantly, but the activation energy of thermal decomposition decreased by 30.07 kJ·mol−1, the characteristic velocities of the laser-induced micro-explosion shock waves increased 12.4 %, the 50 % short-pulse initiation current of the impactor decreased from 3.8 kA to 2.3 kA, and the mechanical sensitivity of DAOAF showed no significant change before and after spherical transformation.

Failure of a detonation wave in a plane channel with multiple obstacles

The results of numerical study of the interaction of a formed cellular detonation wave propagating in a plane channel occupied by a quiescent stoichiometric hydrogen-air mixture with multiple obstacles (barriers) located on the inner surface of the channel are given. The study is carried out to determine the conditions that ensure suppression of detonation. The influence of geometric parameters of the area with obstacles on wave propagation is studied. It is found that localization of the obstacles in a recess in the channel wall leads to a decrease in their destructive effect on detonation. Quenching of detonation combustion by the layer of a non-reacting gas located along the channel wall, limited by single barriers, is considered. The effect of gas composition on the interaction of the detonation wave with the layer is studied. Non-reacting gas mixtures, which, being filled into the area with obstacles, enhance the destructive effect of barriers on the detonation wave are proposed.

The Effects of Material‐Filled Voids on Detonation Wave Shape in Rubberized RDX Explosives

AbstractThe sensitivity of explosives is affected by inhomogeneities within the material. This is evident in the increased shock sensitivity of explosives with slightly lower densities resulting from an increased number of hotspots. The influence of hotspots on explosive initiation has been well studied; however, few studies have been conducted on the effect of intermediate‐sized voids (0.1–10 mm) on a propagating detonation wave. Cylindrical voids filled with air have been studied for diameters ranging from 0.3 mm to 0.8 mm for both 1,3,5,7‐tetranitro‐1,3,5,7‐tetrazocane (HMX) and 1,3,5‐trinitro‐1,3,5‐triazinane (RDX)‐based rubberized explosives. Continuing the investigation into single cylindrical voids, this study examined the effects of 0.5 mm diameter voids filled with different inert cylindrical metals on the detonation wave shape for an RDX‐based rubberized explosive. The metals selected for experiments were 1066 aluminum, brass, copper, and tungsten. The propagation of the detonation wave was captured using a digital streak camera. Experimental results showed that the extent of detonation wave shaping was closely tied to the density differential between the bulk explosive and metal insert. Forty‐four different filler materials, including non‐metals, were simulated using a hydrodynamic code to further analyze material inclusion effects. The main factors hypothesized to be of interest were bulk sound speed, shock impedance, and filler material density. We found that the local detonation delay could be correlated fairly well to a ratio of bulk sound speed and density. Understanding the influence of material inclusions on detonation performance and wave shape allows for tailoring of detonations.

Experimental study on transpiration cooling with phase change in rotating detonation engine

Transpiration cooling with phase change is an effective method for protecting high heat flux walls from ablation in combustion chambers and spaceflight vehicles. The combustion chamber walls of the rotating detonation engine (RDE) experience high heat flux, which poses significant challenges to thermal protection and limits its development. This study introduces a transpiration cooling thermal protection system for a kerosene/air RDE, where the liquid coolant absorbs heat with phase change, reducing wall temperature by more than 50% under certain conditions. The experiments investigated the effects of coolant flow rate, coolant types (water and kerosene), porosity of porous media, and fuel equivalence ratio on both transpiration cooling and detonation wave dynamics. The results show that water provides superior cooling effectiveness compared to kerosene, particularly with increased flow rates and porosity. During RDE operation, increasing flow rates of both water and kerosene initially enhances cooling efficiency but eventually leads to an overall reduction. Furthermore, higher coolant flow rates of both water and kerosene can disrupt the stability of detonation waves within the combustion chamber. Although enlarging the equivalence ratio improves cooling efficiency, maintaining continuous detonation wave generation remains challenging. The cooling efficiency in the detonation combustion mode is lower than that in deflagration. Additionally, carbon deposition was observed in the transpiration cooling system, particularly during prolonged operation. These findings provide valuable insights for the optimization and technical guidance of RDE design.

Experimental study on thermal load characteristics of a U-bend pulse detonation combustor

The performance of pulse detonation turbine engines (PDTE) surpasses that of conventional turbine engines, primarily due to the pressure gain combustion process inherent in PDTE. A U-bend pulse detonation combustor (PDC) with a compact axial length was designed to meet the requirements of PDTE. However, the PDC introduces complex thermal management challenges. In this study, the wall temperature along the U-bend PDC was experimentally measured under various operating conditions, the thermal load characteristics were investigated. The results indicate that the external wall temperature increases monotonically with prolonged operation, whereas the internal wall temperature exhibits periodic fluctuations corresponding to the periodic filling and combustion process in the PDC. The temperature difference between the internal and external walls increases, then decreases over time, eventually fluctuates within a narrow temperature range. The wall temperature was observed to increase along the flow direction, peaking at 811 °C at 30 Hz at the location where the detonation wave is generated. Similarly, the heat flux of the PDC first increases, then decreases, and eventually reaches a constant value, indicating thermal equilibrium. The heat flux represents a significant energy loss, with the detonation section being the area of highest heat loss, reaching approximately 90.5 kW/m2 at 30 Hz.

Influence of metal on the far-exploding surface on fragment deformation behavior under contact explosion

Metals exhibit diverse failure behavior under impact loading. In the context of fragment warheads, preformed fragments also undergo fracture and crushing behaviors when subjected to explosive loading, potentially diminishing the terminal effect and damage capability of the warhead. To address this issue, metal disks of varying impedance were applied to the far-exploding surface of the fragments, and their influence on fragment deformation behavior was examined. The experimental results revealed that when metal disks were attached to the far-exploding surface of the fragments, their fracture behavior changed, and the recovered fragments remained intact axially. Additionally, the axial length of the recovered fragments decreased as the impedance of the metal disk on the far-exploding surface increased. To elucidate the underlying mechanism of this experimental phenomenon, the variation in fragment pressure during the propagation process was calculated by employing theories of planar detonation waves and shock wave propagation in the study. The results indicate that when the impedance of the metal disks on the far-exploding surface is higher than that of the fragments, it leads to an increase in internal pressure and the formation of a compression zone within the fragments, thereby preventing fragment fracture. Conversely, lower impedance results in the formation of a tensile effect within the fragments. The theoretical and experimental results were consistent. Finally, based on the dimensional analysis, the dimensionless models were established to predict fragment deformation and internal pressure values influenced by the metal disk on the far-exploding surface.

Flow-field analysis and performance assessment of rotating detonation engines under different number of discrete inlet nozzles

This study explores in depth rotating detonation engines (RDEs) fueled by premixed stoichiometric hydrogen/air mixtures through two-dimensional numerical simulations including a detailed chemical kinetic mechanism. To model the spatial reactant non-uniformities observed in practical RDE combustors, the referred simulations incorporate different numbers of discrete inlet nozzles. The primary focus here is to analyze the influence of reactant non-uniformities on detonation combustion dynamics in RDEs. By systematically varying the number of reactant injection nozzles (from 15 to 240), while maintaining a constant total injection area, the study delves into how this variation influences the behavior of rotating detonation waves (RDWs) and the associated overall flow field structure. The numerical results obtained here reveal significant effects of the number of inlets employed on both RDE stability (self-sustaining detonation wave) and performance. RDE configurations with a lower number of inlets exhibit a detonation front with chaotic behavior (pressure oscillations) due to an increased amount of unburned gas ahead of the detonation wave. This chaotic behavior can lead to the flame extinguishing or decreasing in intensity, ultimately diminishing the engine's overall performance. Conversely, RDE configurations with a higher number of inlets feature smoother detonation propagations without chaotic transients, leading to more stable and reliable performance metrics. This study uses high-fidelity numerical techniques such as adaptive mesh refinement (AMR) and the PeleC compressible reacting flow solver. This comprehensive approach enables a thorough evaluation of critical RDE characteristics including detonation velocity, fuel mass flow rate, impulse, thrust, and reverse pressure waves under varying reactant injection conditions. The insights derived from the numerical simulations carried out here enhance the understanding of the fundamental processes governing the performance of RDE concepts.

Numerical simulation of detonation propagation and extinction in two-phase gas-droplet ammonia fuel

Numerical simulations of detonation propagation and extinction in ammonia droplet-laden premixed ammonia–oxygen gas are performed in a 2-D planar channel. The sustained propagation and ultimate quenching of detonation with perturbations from ammonia droplets are observed under lower and larger values of initial droplet number density (Nd,0) and diameter (d0), respectively. The detonation always quenches under d0=15μm. The detonation propagation/extinction behaviour and cell structure are dependent on both d0 and Nd,0. The positive correlations between droplet volume fraction, inter-phase mass, momentum, and energy transfers and d0 are more nonlinear than their counterparts of Nd,0. The post-Mach stem region experiences higher-intensity detonative combustion and thus droplet evaporative, accelerative, and heating effects than the post-incident wave region. During the detonation extinction process, the detonation wave degenerates into detonative spots which then decouple into shock and reaction fronts; gaseous pressure, heat release rate, and nitric oxide volume fraction peaks decline.