The re-initiation of cellular detonations downstream of an inert layer

The current work aims to examine how the nature of cellular instabilities controls the re-initiation capability and dynamics of a gaseous detonation transmitting across a layer of inert (or non-detonable) gases. This canonical problem is tackled via computational analysis based on the two-dimensional, reactive Euler equations. Two different chemical kinetic models were used, a simplified two-step induction-reaction model and a detailed model for hydrogen-air. For the two-step model, cases with relatively high and low activation energies, representing highly and weakly unstable cellular detonations, respectively, are considered. For the weakly unstable case, two distinct types of re-initiation mechanisms were observed. (1) For thin inert layers, at the exit of the layer the detonation wave front has not fully decayed and thus the transverse waves are still relatively strong. Detonation re-initiation in the reactive gas downstream of the inert layer occurs at the gas compressed by the collision of the transverse waves, and thus is referred to as a cellular-instability-controlled re-initiation. (2) If an inert layer is sufficiently thick, the detonation wave front has fully decayed to a planar shock when it exits the inert layer, and re-initiation still occurs downstream as a result of planar shock compression only, which is thus referred to as a planar-shock-induced re-initiation. Between these two regimes there is a transition region where the wave front is not yet fully planar, and thus perturbations by the transverse waves still play a role in the re-initiation. For the highly unstable case, re-initiation only occurs via the cellular-instability-controlled mechanisms below a critical thickness of the inert layer. Additional simulations considering detailed chemical kinetics demonstrate that the critical re-initiation behaviors of an unstable stoichiometric mixture of hydrogen-air at 1 atm and 295 K are consistent with the finding from the two-step kinetic model for a highly unstable reactive mixture.     

The study of geometric effects on the explosion front propagation in a horizontal channel with a layer of spherical beads

Experiments were performed in a horizontal channel partially filled with a layer of 12.7 mm ceramic-oxide beads filled with a nitrogen-diluted stoichiometric methane–oxygen mixture, i.e., CH₄ + 2(O₂ + 2/3N₂). Ionization probes and pressure transducers were used to track the explosion front velocity in the 1.22 m long, 76 mm wide and 152 mm high horizontal channel. Schlieren photography and smoked foil techniques are used to gain insight into the explosion front structure. The explosion propagation phenomenon was characterized by the combustion in the bead layer and the unobstructed gap above. It was determined that for a fixed gap height the bead layer thickness had very little effect on the explosion propagation phenomenon. However, for a fixed bead layer height the explosion propagation was strongly influenced by the gap height. The combustion products vented from the bead layer behind the flame propagating in the gap affects the structure of the shock-flame front in the gap and the maximum flame velocity achieved. The coupling between the vented products and the flame velocity in the gap was strongly influenced by the gap height. The gap height also affects the structure of the detonation wave propagating in the gap following DDT that always occurred in the gap. The DDT run-up distance was found to increase with increasing gap height and inversely with initial pressure.     

Detonation propagation across a stratified layer with a diffuse interface

A study was conducted to examine detonation propagation in a stratified layer of hydrogen-oxygen-nitrogen above an inert gas in a horizontal narrow channel. The stratified layer was produced by a gravity current, generated by retracting a door initially separating a hydrogen-oxygen-nitrogen mixture in the predetonator and a heavier inert gas in the test-section. A steady detonation wave generated in the predetonator was transmitted into the stratified layer. The reactivity of the predetonator mixture was varied via the hydrogen-oxygen equivalence ratio and the amount of nitrogen dilution. Schlieren photography was used to visualize the detonation front in the test-section, and soot foils were used to obtain the cellular structure. Schlieren imaging showed a curved detonation front that decoupled at about mid channel height, into a shock wave and trailing contact surface. Both the hydrogen-oxygen-nitrogen reactivity and the type of inert gas initially in the test-section affected the distance travelled by the detonation wave in the stratified layer. The mixture composition distribution within the test-section before ignition was obtained via a three-dimensional CFD simulation. The lateral extent of the cellular structure captured on the soot foil, coincided with the calculated inert gas mole fraction contour that corresponds to a sharp increase in the ZND induction zone length, e.g., 70% argon dilution for a stoichiometric hydrogen-oxygen predetonator mixture.     

The influence of multi-layer confinement on detonation propagation in condensed-phase explosives

We examine, via multi-material simulation in a two-dimensional planar geometry, the effects on steady detonation propagation of the presence of a low-density intermediate layer between a condensed-phase high explosive (HE) and a high-density metallic confiner of finite thickness. Such elastomer intermediate layers are often added to eliminate air-gaps and the associated jetting effects that can arise due to machining imprecisions, or to prevent HE cracking due to environmental changes. Without an intermediate layer, the flow structure of a steady detonation/metal confiner interaction is well understood. In particular, there is no reflected wave passed into the HE due to the metal confinement. With the elastomer layer present, we find that, as the intermediate layer width increases, a complex wave interaction and communication path develops between the HE, intermediate, and metal layers. For thin intermediate layers, a shock-driven subsonic flow develops in the intermediate layer, passing information from the metal layer to the HE, with the detonation speed decreasing as the intermediate layer width increases. For wider intermediate layers, a Mach stem configuration develops in the intermediate layer, forcing a shock to be reflected into the HE. Simultaneously, a localized Prandtl-Meyer fan emerges from the intersection of the detonation shock with the HE-intermediate layer material interface. These HE structures are shown to have a substantial effect on the structure of the detonation driving zone. The Prandtl-Meyer fan becomes the dominant structure for critically large intermediate layer widths, wherein the presence of the metal layer does not affect the detonation propagation. We examine the detonation propagation speed and reaction and driving zone structure as a function of varying intermediate layer width. Two confinement metals are examined, along with two high explosive and three metal layer widths.     

Deflagration to detonation transition in fast flames and tracking with chemical explosive mode analysis

In the context of vapour cloud explosion, the flame acceleration process can lead to conditions promoting deflagration to detonation transition (DDT), potentially leading to increased damages in accidental scenarios. This study focuses on this phenomenon by performing simulations of detonation reinitiation for fast flames in the Chapman–Jouguet deflagration regime. It is obtained experimentally by the attenuation of an incident detonation by an array of obstacles. A primary objective of the paper is to demonstrate the ability of the numerical model to reproduce the major experimental trends, namely the variation of the reinitiation propensity for different initial pressures and blockage ratios (BRs). Chemical explosive mode analysis (CEMA) is also adapted to the context of this study, in order to identify locally the propagation regime and to provide insights on the reinitiation mechanism. An a priori validation of the CEMA methodology is first performed on relevant canonical one-dimensional configurations. Subsequently, ensembles of five realizations are computed at different initial pressures and BRs and compared to experimental data. They are shown to reproduce the major observed trends in terms of detonation reinitiation length with respect to the operating conditions, with significant variability from one realization to another. In addition, the reinitiation mechanism is also found to be consistent with experimental observations and a previous numerical study of the same configuration. The CEMA methodology adapted to this context is able to identify locally the different propagation regimes, and to track the highly reactive zones that coherently couple with transverse pressure perturbations, leading to the formation of a strongly reacting kernel which eventually triggers the detonation reinitiation.     

Propagation of detonation in fuel–air mixtures in flat channels

The wide scatter of the values of the measured detonation cell size in fuel + air mixtures restricts the applicability of this parameter in the estimation of the geometric limits of detonation propagation, including in rectangular channels whose height is much larger than their width. The critical channel height for the propagation of detonation has been experimentally determined for hydrogen + air, propane + air, and ethylene + air mixtures. In order to reveal the specific features of the propagation and decay of detonation in a narrow channel, numerical simulation has been carried out for a hydrogen + air mixture with account taken of the cellular structure of the detonation wave.     

Experimental investigation and numerical validation of explosion suppression by inert particles in large-scale duct

A large-scale duct with an explosion suppressor was designed to investigate experimentally the explosion suppression by inert particles for a CH₄/O₂/N₂ mixture. The duct is 25 m long and has an internal diameter of 700 mm. Pressure and flame signals were recorded some distance away from ignitor in the duct. Pressure tracking lines of the shock front for the different inert particle cloud densities and the inert particle diameters were made. The measured results indicate that the shock front is decoupled from the flame front in the inert particle cloud, which leads to a suppression of explosion. Also, the experiments suggest that increasing the inert particle cloud density or decreasing the inert particle diameter can enhance the ability to suppress explosion. For the purpose of validation, a two-dimensional numerical model coupled with the element chemical reaction mechanism for the simulations of the CH₄/O₂/N₂ mixture explosion suppression by the inert particles has been developed. This model makes use of the second-order TVD scheme and the MacCormack scheme to calculate gas-phase and particle-phase equations, respectively. The Strang splitting technique is used to treat the stiffness due to the coupling of the governing equations, while the implicit Gear algorithm is used to treat the stiffness due to the chemical reactions. The effect of inert particle cloud density on explosion suppression was investigated using the model. The calculated results indicate that the accumulation of inert particles slows the propagation of the gas-phase shock front and results in explosion suppression. With increased inert particle cloud density, the explosion suppression is more prominent. The calculated results show a qualitative agreement with the measured results in the large-scale duct experiment.     

氢氧爆轰波在激波管中的成长机制研究

 针对气相爆轰波成长机制研究,采用压力传感器和高速摄影技术,测试了氢氧混合气体在点火后的火焰波、前驱冲击波以及爆轰波的成长变化过程,计算了冲击波过程参数和气体状态参数,分析了火焰加速机制。实验结果表明,APX-RS型高速摄影系统可用于拍摄气相爆轰波的成长历程;氢氧爆轰波的产生是由于湍流火焰和冲击波的相互正反馈作用,导致反应区内多处发生局部爆炸,爆炸波与冲击波相互耦合,最终成长为定常爆轰波。     

Effect of boundary layer losses on 2D detonation cellular structures

We evaluate the effect of boundary layer losses on two-dimensional H2/O2/Ar cellular detonations obtained in narrow channels. The experiments provide the details of the cellular structure and the detonation speed deficits from the ideal CJ speed. We model the effect of the boundary layer losses by incorporating the flow divergence in the third dimension due to the negative boundary layer displacement thickness, modeled using Mirels’ theory. The cellular structures obtained numerically with the resulting quasi-2D formulation of the reactive Euler equations with two-step chain-branching chemistry are found in excellent agreement with experiment, both in terms of cell dynamics and velocity deficits, provided the boundary layer constant of Mirels is modified by a factor of 2. A significant increase in the cell size is found with increasing velocity deficit. This is found to be very well captured by the induction zone increase in slower detonations due to the lower temperatures in the induction zone.     

Flame acceleration and transition to detonation: Effects of a composition gradient in a mixture of methane and air

The effects of a composition gradient on flame acceleration and transition to detonation in a mixture of methane and air were studied by numerically solving the unsteady, fully compressible, reactive Navier–Stokes equations. The specific problem addressed here is for ignition in a two-dimensional, obstructed channel where there is a spatial gradient of equivalence ratios perpendicular to the propagation direction of the reaction wave. The solution method uses a calibrated, optimized chemical-diffusive model that reproduces correct flame and detonation properties for methane–air mixtures over a range of equivalence ratios. Comparisons were made to a stoichiometric, homogeneous mixture in order to focus on the worst-case scenario for safety concerns. The results showed that the flame speed is smaller and the average total heat release are lower, but the maximum flame surface area is larger in the inhomogeneous mixture. This is because there is more unburned material between obstacles but less energy released from this increased flame surface area in the fuel-lean region, leading to the reduction of the total heat release. The transition to detonation is delayed in the inhomogeneous mixture, because the hot spot forms in the fuel-lean region and the strength of the Mach stem that hits the obstacle is weaker. The detonation front tends to decouple into a shock and a flame earlier in the inhomogeneous mixture, due to the incomplete mixing throughout the entire domain during the detonation propagation process.     

Detonation simulations in supersonic flow under circumstances of injection and mixing

The unsteady, reactive Navier-Stokes equations with a detailed chemical mechanism of 11 species and 27 steps were employed to simulate the mixing, flame acceleration and deflagration-to-detonation transition (DDT) triggered by transverse jet obstacles. Results show that multiple transverse jet obstacles ejecting into the chamber can be used to activate DDT. But the occurrence of DDT is tremendously difficult in a non-uniform supersonic mixture so that it required several groups of transverse jets with increasing stagnation pressure. The jets introduce flow turbulence and produce oblique and bow shock waves even in an inhomogeneous supersonic mixture. The DDT is enhanced by multiple explosion points that are generated by the intense shock wave focusing of the leading flame front. It is found that the partial detonation front decouples into shock and flame, which is mainly caused by the fuel deficiency, nevertheless the decoupled shock wave is strong enough to reignite the mixture to detonation conditions. The resulting transverse wave leads to further mixing and burning of the downstream non-equilibrium chemical reaction, resulting in a high combustion temperature and intense flow instabilities. Additionally, the longitudinal and transverse gradients of the non-uniform supersonic mixture induce highly dynamic behaviors with sudden propagation speed increase and detonation front instabilities.     

Propagation of Cellular Modes of Titanium-Powder Layer Combustion in Air Channels,Allowing for the Effect of Natural Convection of Gas

In this paper, we have studied the effect of impurity and inert gases on the formation and propagation of cellular-combustion regimes for their inhomogeneous distribution above the surface of the reacting metal layer. The gas-dynamic aspects of the formation and steady propagation of inhomogeneous wave structures in the combustion of a titanium powder layer in through and semi-closed inclined air canals and in channels with uneven loading are considered. The gas composition heterogeneity over the reaction zone and the gas stratification, i.e., the stratification of a gas mixture of different densiies above the reacting layer, are shown to lead to the formation of inclined non-uniform and cellular fronts under conditions of a lack of active gas in the reaction zone and the loss of stability of the planar front.     

Transverse wave generation mechanism in rotating detonation

Detonation engines are expected to be included in a number of aerospace thrusters in the future. Several types of detonation engines are currently under examination, including the rotating detonation engine (RDE). Although the RDE has been explored experimentally, its rotating detonation propagation mechanism is not well understood. This paper clarifies the detonation mechanism and dynamics of the RDE by 2D and 3D simulation using compressible Euler equations with a full chemical reaction mechanism of H₂/O₂ and H₂/Air, especially from the triple-point and transverse detonation points of view. A total variation diminishing (TVD) scheme is used for the mixture of H₂/Air, and an advection upwind splitting method difference vector (AUSMDV) scheme is used for the mixture of H₂/O₂. The use of an AUSMDV scheme provides a much clearer detonation structure than does the TVD scheme. We focus on the complex interaction mechanism of the detonation front and burned mixture gases. We found out that at this interaction point, an unreacted gas pocket appears and ignites periodically to generate transverse waves at the detonation front and maintain detonation propagation.     

A flame technique to isolate the detonation/product interface relevant to rotating detonation engines

A novel experimental technique is proposed to study the detonation propagation in a layer of non-reacted gas weakly confined by combustion products. This problem is relevant to rotating detonation engines, where transverse detonations are confined by products of a previous rotation cycle, and other applications such as industrial safety. The experimental technique utilizes a flame ignited along the top wall in a long channel. The preferential growth of the flame along the long direction of the channel creates a finger flame and permits to create a narrow layer of unburned gas. A detonation ignited outside of this layer then propagates through the layer. This permits to conduct accurate observations of the detonation interaction with the inert gas and determine the boundary condition of the interaction. The present paper provides a proof-of-concept demonstration of the technique in a 3.4 m by 0.2 m channel, in which long finger flames were observed in ethylene-oxygen mixtures. The flame is visualized by high-speed direct luminosity over its entire travel, coupled with pressure measurements. A direct simulation of the flame growth served to supplement the experiments and evaluate the role of the induced flow by the flame growth, which gives rise to a non-uniform velocity distribution along the channel length. Detonation experiments were also performed at various layer heights in order to establish the details of the interaction. The structure was visualized using high speed Schlieren video. It was found that an inert shock always runs ahead of the detonation wave, which gives rise to a unique double shock reflection interaction.     

Modelling detonation of heterogeneous explosives with embedded inert particles using detonation shock dynamics: Normal and divergent propagation in regular and simplified microstructure

This paper discusses the mathematical formulation of Detonation Shock Dynamics (DSD) regarding a detonation shock wave passing over a series of inert spherical particles embedded in a high-explosive material. DSD provides an efficient method for studying detonation front propagation in such materials without the necessity of simulating the combustion equations for the entire system. We derive a series of partial differential equations in a cylindrical coordinate system and a moving shock-attached coordinate system which describes the propagation of detonation about a single particle, where the detonation obeys a linear shock normal velocity-curvature (D_n–κ) DSD relation. We solve these equations numerically and observe the short-term and long-term behaviour of the detonation shock wave as it passes over the particles. We discuss the shape of the perturbed shock wave and demonstrate the periodic and convergent behaviour obtained when detonation passes over a regular, periodic array of inert spherical particles.     

Multilevel detonation cell structures in methane-air mixtures

High-resolution numerical simulations of two-dimensional detonations in a methane-air mixture with extremely high activation energy show the formation of multiple levels of cellular structures caused by the propagation of triple-shock configurations. Two main types of these configurations were observed based on the structure of transverse waves behind the leading edge of the detonation. Collisions were observed between two triple-shock configurations with attached transverse detonations, two triple-shock configurations with inert transverse waves, and one of each of these types. These collisions give rise to the formation of highly irregular, and, in some cases incomplete, cells. Smoke foils obtained from detonation of a near-stoichiometric mixture of natural gas and air show similar results. Estimates of the width of the experimental cells qualitatively match those inferred from the calculations.     

An experimental investigation of the propagation mechanism of critical deflagration waves that lead to the onset of detonation

The reflection of a CJ detonation from a perforated plate is used to generate high speed deflagrations downstream in order to investigate the critical conditions that lead to the onset of detonation. Different perforated plates were used to control the turbulence in the downstream deflagration waves. Streak Schlieren photography, ionization probes and pressure transducers are used to monitor the flow field and the transition to detonation. Stoichiometric mixtures of acetylene–oxygen and propane–oxygen were tested at low initial pressures. In some cases, acetylene–oxygen was diluted with 80% argon in order to render the mixture more “stable” (i.e., more regular detonation cell structure). The results show that prior to successful detonation initiation, a deflagration is formed that propagates at about half the CJ detonation velocity of the mixture. This “critical” deflagration (which propagates at a relatively constant velocity for a certain duration prior to the onset of detonation) is comprised of a leading shock wave followed by an extended turbulent reaction zone. The critical deflagration speed is not dependent on the turbulence characteristics of the perforated plate but rather on the energetics of the mixture like a CJ detonation (i.e., the deflagration front is driven by the expansion of the combustion products). Hence, the critical deflagration is identified as a CJ deflagration. The high intensity turbulence that is required to sustain its propagation is maintained via chemical instabilities in the reaction zone due to the coupling of pressure fluctuations with the energy release. Therefore, in “unstable” mixtures, critical deflagrations can be supported for long durations, whereas in “stable” mixtures, deflagrations decay as the initial plate generated turbulence decays. The eventual onset of detonation is postulated to be a result of the amplification of pressure waves (i.e., turbulence) that leads to the formation of local explosion centers via the SWACER mechanism during the pre-detonation period.     

Initiation and propagation of detonation waves in combustible high speed flows

The initiation and propagation of detonation waves in combustible high speed flows were studied experimentally. A planar detonation wave traveling in an initiation tube was transmitted into a test section where a combustible high speed flow was induced by an incident shock wave generated in a shock tube. In this study, the flow Mach numbers were obtained as 0.9 and 1.2. The experimental results show that depending on the flow velocity, the apparent propagation velocity of a detonation wave is higher in the upstream and lower in the downstream direction than the CJ velocity. Smoked plate records reveal cellular patterns deformed in the flow direction, and the calculated aspect ratios of the cell were found to agree well with the experimental ones on the basis of the assumption that the velocity of the transverse wave is not affected by the flowing mixture. By analyzing the shock-wave diffraction at the position where there is an abrupt change in the area, on the basis of Whitham’s theory, it was deduced that in the present experimental set-up, the detonation was initiated by the reflection of the diffracted shock waves on the sidewalls of the test section. The agreement between the experimental and calculated results regarding the position of the cellular patterns on the smoked plate record indicated that the position of detonation initiation in high speed flows is shifted downstream due to the flow velocity.     

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.     

Calibration of the Pseudo-Reaction-Zone model for detonation wave propagation

An approach for the calibration of an advanced programmed burn (PB) model for detonation performance calculations in high explosive systems is detailed. Programmed burn methods split the detonation performance calculation into two components: timing and energy release. For the timing, the PB model uses a Detonation Shock Dynamics (DSD) surface propagation model, where the normal surface speed is a function of local surface curvature. For the energy release calculation and subsequent hydrodynamic flow evolution, a Pseudo-Reaction-Zone (PRZ) model is used. The PRZ model is similar to a reactive burn model in that it converts reactants into products at a finite rate, but it has a reaction rate dependent on the normal surface speed derived from the DSD calculation. The PRZ reaction rate parameters must be calibrated in such a way that the rate of energy release due to reaction in multi-dimensional geometries is consistent with the timing calculation provided by the DSD model. Our strategy for achieving this is to run the PRZ model in a detonation shock-attached frame in a compliant 2D planar slab geometry in an equivalent way to a reactive burn model, from which we can generate detonation front shapes and detonation phase speed variations with slab thickness. In this case, the D _n field used by the PRZ model is then simply the normal detonation shock speed rather than the DSD surface normal speed. The PRZ rate parameters are then iterated on to match the equivalent surface front shapes and surface phase speed variations with slab thickness derived from the target DSD model. For the purposes of this paper, the target DSD model is fitted to the performance properties of an idealised condensed-phase reactive burn model, which allows us to compare the detonation structure of the calibrated PRZ model to that of the originating idealised-condensed phase model.