Shock Focusing Research Articles

Numerical study on flame acceleration and deflagration-to-detonation transition: Spatial distribution of solid obstacles

This study conducts a detailed numerical investigation on the spatial distribution of solid obstacles using the large eddy simulation method. It is discovered that although flame acceleration induced by solid obstacles is dominated by factors such as flow field disturbances, vortices and recirculation zones, turbulence, flame surface areas and combustion heat release rates, etc., the characteristics of the leading shock wave are key to detonation initiation. Specifically, the intensity of the leading shock wave, its formation time, and its distance from the flame front significantly affect detonation initiation. Depending on the state of the shock wave, the detonation initiation process may occur through various mechanisms such as shock reflection, shock focusing. Overall, the types of detonation initiation in this study all belong to the shock detonation transition. However, the detonation initiation process can be further classified into two categories: (I) Detonation induced by shock wave reflection; (II) detonation triggered by shock wave focusing. Despite certain disparities in the detonation initiation process, all detonation initiation processes conform to the gradient theory, and the flame evolution processes in all cases consistently follow three stages: the laminar slow-ignition stage; the turbulent deflagration stage; the detonation initiation stage. Furthermore, the study further discerns that, compared to positioning obstacles on the wall, placing obstacles inside the combustion chamber can further augment the detonation-assisting effect. However, excessively sparse or dense spatial distributions of solid obstacles fail to yield the optimal detonation effect. An optimal distribution exists, which triggers the fastest detonation initiation.

Modal Discontinuous Galerkin Simulations of Richtmyer–Meshkov Instability at Backward-Triangular Bubbles: Insights and Analysis

This paper investigates the dynamics of Richtmyer–Meshkov instability (RMI) in shocked backward-triangular bubbles through numerical simulations. Two distinct gases, He and SF6, are used within the backward-triangular bubble, surrounded by N2 gas. Simulations are conducted at two distinct strengths of incident shock wave, including Ms=1.25 and 1.50. A third-order modal discontinuous Galerkin (DG) scheme is applied to simulate a physical conservation laws of two-component gas flows in compressible inviscid framework. Hierarchical Legendre modal polynomials are employed for spatial discretization in the DG platform. This scheme reduces the conservation laws into a semi-discrete set of ODEs in time, which is then solved using an explicit 3rd-order SSP Runge–Kutta scheme. The results reveal significant effects of bubble density and Mach numbers on the growth of RMI in the shocked backward-triangular bubble, a phenomenon not previously reported. These effects greatly influence flow patterns, leading to intricate wave formations, shock focusing, jet generation, and interface distortion. Additionally, a detailed analysis elucidates the mechanisms driving vorticity formation during the interaction process. The study also thoroughly examines these effects on the flow fields based on various integral quantities and interface characteristics.

Exploring the Atwood number impact on shock-driven hydrodynamic instability at pentagonal interface using discontinuous Galerkin simulations

Investigation of Atwood number impact is crucial for comprehending the flow dynamics of the evolving hydrodynamic instability. In this paper, the Atwood number impacts on the shock-driven hydrodynamic instability at a backward-facing pentagonal interface in its early stages are explored numerically. The shock-driven pentagonal interface has a unique property in which the incident angle of the shock wave is constant along the interface edge. This property provides the ideal environment for the shock-refraction process. To examine the Atwood number impact, we consider five distinct gases, including sulfur hexafluoride, krypton, argon, neon, and helium, which are filled inside the pentagonal interface and surrounded by nitrogen gas. A mixed modal discontinuous Galerkin method is used to solve the two-dimensional Navier–Stokes–Fourier equations for two-component gas flows for numerical simulations. The simulation results illustrate that the Atwood number plays a crucial role in the flow fields of the shocked-pentagonal gas interface, which have not been reported in the literature. The flow fields are greatly impacted by the Atwood number, leading to complex wave patterns, shock focusing, jet formation, interface deformation, and vorticity generation. Further, the Atwood number effects on the flow fields are also thoroughly examined by a quantitative study based on the integral quantities and the interface features. Finally, a quantitative analysis is performed to examine the intrinsic differences between the evolution of the flow fields at the square and pentagonal interfaces.

Transition to detonation in hydrogen-air mixtures due to shock focusing in a 3-wall 90-deg corner

This work presents an experimental investigation on the transition to detonation due to shock-wave focusing in a 3-wall 90-deg corner in hydrogen-air mixtures (17.5 – 60% H2) initially at 298 K and 1 bara. The reflector was placed at one side of 2 – m long, 0.14 m internal diameter tube. The other side of the tube was equipped with an ignition source and a flame acceleration section. The shock wave approached the reflector with a velocity in the range of 580 – 970 m/s. The reflector was placed symmetrically to the tube axis. The research proved that transition to detonation due to shock focusing highly depends on the shock wave strength and can be triggered in a stoichiometric mixture at shock speed VS = 605 m/s which corresponds to M = 1.485 or 59.9% of the speed of sound in combustion products. The ignition delay time recorded for transition to detonation was at the order of few microseconds. The detonability range observed with the 3-wall 90-deg reflector proved to be 15 - 70 % H2 in air compared to 18 - 59% H2 observed in work performed for a 90-deg wedge reflector configuration at the same initial conditions. Additionally, the scaling factor between critical shock velocity between both types of reflectors is almost constant and equal to 0.84 throughout the investigated mixtures. The high focusing ability of the 3-wall corner has also proved the minimum transition pressure recorded in the corner tip at the level of 8.95 MPa in a stoichiometric mixture. This value corresponds to a nearly 17-fold increase in pressure compared to normal shock post-reflection conditions. Considering the shock focusing as the major trigger for detonation the presented results may explain the differences between the detonability limits observed in obstacle-laden ducts and large-scale experimental setups.

Experimental demonstration on detonation initiation by laser ignition and shock focusing in elliptical cavity

As a method of initiating detonation in a short distance with a small amount of energy, the combination of laser ignition and shock focusing in an elliptical cavity was proposed and experimentally demonstrated with a C2H4-O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {C}_{2}\\hbox {H}_{4}{-}\\hbox {O}_{2}$$\\end{document} mixture at 100 kPa and 297 K. In the experiment, an elliptical cavity and single rectangular cavities of different heights were used, and their flow-field patterns were visualized using high-speed schlieren imaging. Detonation initiation was achieved in the case of the elliptical cavity, and based on the Mach number change of the leading shock wave, two propagation phases were verified: the deceleration and acceleration phases. The deceleration phase was driven merely by the gasdynamic effect, wherein the initial shock wave (ISW) expanded spherically, and the acceleration phase began when the ISW shifted to planar propagation. In the acceleration phase, although gradual acceleration was observed in rectangular cavities, rapid acceleration occurred in the elliptical cavity. From the schlieren images, the second acceleration was caused not only by the concave reflected shock wave’s catching up with the ISW, but also by the fast-flames that were generated along the cavity corners and engulfed the ISW in the converging section of the elliptical cavity.

Numerical investigation of the pressure gain obtained by the double-stage JP-10/air detonation wave

In this study, a double-stage detonation system is proposed to achieve higher pressure gain. The first-stage detonation transforms into a shock when it passes through a thin inert layer. Subsequently, this shock compresses the second-stage unburnt mixture, increasing its initial pressure. Finally, the second-stage detonation is initiated, resulting in higher pressure gain. One- and two-dimensional transient numerical simulations of the JP-10/air detonation wave are conducted, coupled with the global reaction model developed by the authors. The numerical model and methods are validated by comparing the combustion and detonation properties with both detailed reaction kinetics and experimental data. The results demonstrate that the peak pressure of the second-stage detonation wave is twice as high as that of the first-stage detonation wave. This finding proves that compared to a single detonation wave, higher pressure gain can be achieved by implementing the current double-stage detonation wave. To address the complexity arising from multi-detonation initiation, the second-stage detonation combustor is optimized by achieving detonation self-initiation through shock focusing. Numerical simulations further confirm the feasibility of this process. The results indicate that the detonation pressure near the shock focusing zone is much higher than in the rest of the zone, and the detonation is in an over-driven state during the early stages after shock focusing.

Computational diagnostics for flame acceleration and transition to detonation in a hydrogen/air mixture

A new computational diagnostic method for pressure-induced compressibility is proposed by projecting its local contribution to the chemical explosive mode (CEM) in the chemical explosive mode analysis (CEMA) framework. The new method is validated for the study of detonation development during the deflagration-to-detonation transition (DDT) process. The flame characteristics are identified through the quantification of individual CEM contributions of chemical reaction, diffusion, and pressure-induced compressibility. Numerical simulations are performed to investigate the DDT processes in a stoichiometric hydrogen-air mixture. A Godunov algorithm, fifth-order in space, and third-order in time are used to solve the fully compressible Navier-Stokes equations on a dynamically adapting mesh. A single-step, calibrated chemical diffusive model (CDM) described by Arrhenius kinetics is used for energy release and conservation between the fuel and the product. The new diagnostic method is first applied to one-dimensional (1D) canonical flame configurations followed by two-dimensional (2D) simulations of DDT in an obstructed channel where different detonation initiation scenarios are examined using the new CEMA projection formulation. Detailed examinations of the idealized configuration of detonation initiation through shock focusing mechanism at a flame front are also studied using the new formulation. A comparison of the currently proposed CEMA projection and the original formulation by the authors suggests that including the pressure-induced compressibility is essential for the use of CEMA in DDT process. The results also show that the new formulation of CEMA projection can successively capture the detonation initiation through either a gradient mechanism or a direct initiation mechanism, and therefore can be used as an effective local analytical tool for the computational diagnostics of detonation initiation in a DDT process. It was found that detonation development is characterized by a strong contribution of chemistry role to the CEM which is pivotal to the initiation of detonation. The role of compressibility is found enhanced at the edge of the detonation front where diffusion was found to have minimal effects on detonation development. Novelty and Significance StatementA new computational diagnostic method for pressure-induced compressibility is proposed by projecting its local contribution to the chemical explosive mode (CEM) in the chemical explosive mode analysis (CEMA) framework. The proposed method is tested and validated for the study of detonation development during the deflagration to detonation transition (DDT) process. The new method is found to be an effective local analytical tool for the computational diagnostics of detonation initiation in a DDT process. The proposed method is versatile and can be used on various different platforms which makes this study more impactful.

High-power laser beam shaping using a metasurface for shock excitation and focusing at the microscale.

Achieving high repeatability and efficiency in laser-induced strong shock wave excitation remains a significant technical challenge, as evidenced by the extensive efforts undertaken at large-scale national laboratories to optimize the compression of light element pellets. In this study, we propose and model a novel optical design for generating strong shocks at a tabletop scale. Our approach leverages the spatial and temporal shaping of multiple laser pulses to form concentric laser rings on condensed matter samples. Each laser ring initiates a two-dimensional focusing shock wave that overlaps and converges with preceding shock waves at a central point within the ring. We present preliminary experimental results for a single ring configuration. To enable high-power laser focusing at the micron scale, we demonstrate experimentally the feasibility of employing dielectric metasurfaces with exceptional damage threshold, experimentally determined to be 1.1 J/cm2, as replacements for conventional optics. These metasurfaces enable the creation of pristine, high-fluence laser rings essential for launching stable shock waves in materials. Herein, we showcase results obtained using a water sample, achieving shock pressures in the gigapascal (GPa) range. Our findings provide a promising pathway towards the application of laser-induced strong shock compression in condensed matter at the microscale.

Numerical investigation of shock Mach number effects on Richtmyer–Meshkov instability in a heavy square bubble

This study conducts a two-dimensional numerical investigation of incident shock Mach number effects on the Richtmyer–Meshkov (RM) instability after a shock wave impulsively drives a heavy square bubble. The square bubble is composed of SF6 gas, which is surrounded by nitrogen gas. Five different shock Mach numbers are considered: Ms=1.12, 1.22, 1.4, 1.7, and 2.1. Two-dimensional compressible Euler equations for two-component gas flows are simulated with a high-order modal discontinuous Galerkin solver. For validation, the numerical results are compared with the existing experimental results and are found to be in good agreement. The present results reveal that the incident shock Mach number is critical in the growth of RM instability in a heavy square bubble. The shock Mach number affects flow morphology significantly, resulting in complicated wave patterns, shock focusing, jet creation, bubble deformation, and vorticity generation. The convergent shape of the bubble causes shock focusing, which creates a local high-pressure zone and, as a result, an outward jet generation. It is found that the bubble deforms differently with increasing shock Mach number, and the different shock Mach numbers alter the distance between the shock focusing position and the downstream bubble interface. The effects of shock Mach numbers are investigated in depth through physical phenomena such as vorticity production, kinetic energy, and enstrophy. Finally, the shock Mach number impacts on the time-variations of the shock trajectories and interface structure are thoroughly investigated.

Transmission of hydrogen detonation across a curtain of dilute inert particles

Transmission of hydrogen detonation wave (DW) in an inert particle curtain is simulated using the EulerianLagrangian approach. A detailed chemical mechanism is used to predict the detonative combustion of a stoichiometric hydrogen-air mixture and parametric studies are conducted based on a two-dimensional computational domain. A detonation map of propagation and extinction corresponding to various particle sizes, concentrations, and curtain thicknesses is plotted. It is shown that the critical curtain thickness decreases considerably when the particle concentration is less than the critical value. The effects of curtain thickness on the trajectories of peak pressure, shock front speed, and heat release rate are examined. Three propagation modes of the DW in particle curtain are found: detonation transmission, partial extinction and detonation re-initiation, as well as detonation extinction. The first two modes are analyzed with the evolutions of shock frontal structures and chemical explosive mode. The chemical explosive mode analysis confirms that a detonation re-initiation event is caused by a re-initiation point with high pressure and explosive propensity, resulting from transverse shock focusing. The influence of particle dimeter/concentration, and curtain thickness on the DW are also examined with peak pressure trajectories, shock speed, and interphase exchange rates of energy and momentum. In addition, small variations of the curtain thickness will affect the short-term behaviors of detonation development, but the long-term DW behaviors are negligibly affected. Furthermore, the evolutions of curtain morphologies are analyzed by the particle velocity, volume fraction, Stokes drag and Archimedes force. This analysis confirms the importance of drag force in influencing the curtain morphologies. Different curtain evolution regimes are found: quasi-stationary regime, shrinkage regime, constant-thickness regime, and expansion regime. Finally, the influences of the curtain thickness on the characteristic time of curtain evolutions are studied. It is found that all characteristic time become smaller when the curtain thickness increases.

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

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

Effects of staggered opposed hot jets on the initiation and propagation of gaseous detonation in a supersonic combustible inflow

In this paper, the detonation initiation mechanism of a supersonic combustible mixture triggered by a staggered opposing combined hot jets was performed. Two-dimensional reactive Navier–Stokes equations with a one-step Arrhenius chemistry model were solved using a structured adaptive mesh refinement framework. The results show that a high temperature and pressure region triggers a rapid detonation initiation after the jet-induced bow shock focusing. Further analysis showed that there is a large baroclinic torque behind the local detonation wave induced by the staggered hot jet, which leads to a large Richtmyer–Meshkov instability at the end of the unburned jet, and the generated periodic shedding vortex structure thereby enhances the diffusion effect in the unburned region. However, the released heat cannot support the propagation of the detonation wave. In addition, different jet intensity distribution schemes and jet spacing will change the ignition point position. It is worth noting that the distance of detonation initiation can be significantly shortened by reducing the front jet intensity while maintaining the total jet energy. Increasing the jet spacing will significantly slow down the detonation initiation process.

Eulerian–Lagrangian modeling of deflagration to detonation transition in n-decane/oxygen/nitrogen mixtures

In this work, to promote deflagration to detonation transition (DDT), a designed hot jet in a pre-detonator is produced to initiate detonations in the main detonation tube. We perform two-dimensional simulations of the DDT process for low-volatile fuel (n-decane) mixed with nitrogen and oxygen based on the Eulerian–Lagrangian approach. The effects of fuel atomization, vaporization, and shock focusing on the flame acceleration and DDT are discussed under different nitrogen dilution ratio and droplet size conditions. The results show that the flame acceleration process can be divided into slow and fast deflagration stages. Additionally, initiation times are mainly determined by the fuel atomization and evaporation in the slow deflagration stage, which dominates the entire DDT time. Furthermore, there are different intensities of hot jets rather than stable detonation waves formed at the pre-detonator exit. Moreover, local decoupling and re-initiation events are detected near the internal wall of the U-bend, inducing the overdriven detonation decaying into stable detonation waves in the smooth tube. The results also demonstrate that the detonation pressure and velocity decrease by 13.56% and 12.55%, respectively, as the nitrogen dilution ratio increases from 0.5 to 2. In particular, as the nitrogen dilution ratio continued to increase to 2.25, the development in DDT is similar, but the jet intensity is significantly weakened. While as the droplet size increases from 10 to 40 μm, the detonation pressure and velocity decrease only by 2.69% and 1.49%, respectively.

Visualization of ignition modes in methane-based mixture induced by shock wave focusing

In this study, different ignition modes and detonation initiation due to shock wave focusing are observed by combining a transient overpressure recording technique and a high-speed schlieren photography system. In plane reflection, only weak and strong ignition modes are observed; while there are three ignition modes in the 90-degree and 60-degree wedges by introducing shock wave focusing: peak local ignition mode (PLIM), boundary ignition mode (BIM), and strong ignition mode (SIM). In PLIM, the flame is generated at the apex of the wedge-shaped reflector, but the propagation speed is slow, the flame area concentrates on the apex of the reflector and maintains for a long time. In BIM, the flame is firstly generated at the apex of the wedge and quickly propagates along the tube wall; later the flame propagates slowly from the tube wall to the central unburned area. In SIM, oblique shock waves are generated when the shock waves are reflected from the wedged walls, the interaction of oblique shocks inducing the initiation of detonation. In addition, the incident shock velocity (Vi) range corresponding to different ignition modes for different shock wave focusing types is given. The lower velocity limit of SIM for planar, 90-degree, and 60-degree wedge reflectors is 980 m/s, 915 m/s, and 880 m/s, respectively. Therefore, it is more conducive to initiate the detonation wave in the 60-degree wedge with a lower speed shock wave. The instantaneous maximum pressure (Pmax) and maximum pressure after ignition (Pign) of the three reflectors are investigated corresponding to each ignition mode. It is found that Pign and Pmax can be used to determine SIM. This study provides new insight into different ignition modes in wedge reflectors due to shock focusing; the results are beneficial to understanding the physics of shock wave focusing and its mechanism of shock focusing-induced detonation.

Interactions between a propagating detonation wave and circular water cloud in hydrogen/air mixture

Interactions between a propagating hydrogen/air detonation wave and circular water cloud are studied. Eulerian-Lagrangian method involving two-way gas-droplet coupling is applied. Different droplet (diameter, concentration) and cloud (diameter) properties are considered. Results show that droplet size, concentration and cloud radius have significant effects on peak pressure trajectory of the detonation wave. Three propagation modes are identified: perturbed propagation, leeward re-detonation, and detonation extinction. Leeward re-detonation is analyzed from unsteady evolutions of gas and liquid droplet quantities. The detonation is re-initiated by a local hot spot from shock focusing of upper and lower diffracted detonations. Disintegration of water droplets proceeds when the detonation wave crosses the cloud. In addition, detonation extinction is featured by quickly fading peak pressure trajectories when the detonation wave passes the larger cloud, and no local autoignition occurs in the shock focusing area. Evolutions of thermochemical structures from the shocked area in an extinction process are also studied. The transfer rates of mass, energy and momentum of detonation success and failure are analyzed. Moreover, parametric studies demonstrate that the critical cloud size to quench a detonation decreases when the droplet concentration is increased. However, when the droplet concentration is beyond 0.84 kg/m3, the critical cloud size is negligibly influenced due to small droplets. Two-phase fluid interfacial instability is observed, and the mechanism of cloud evolution is studied with the distributions of droplet, vorticity, density / pressure gradient magnitudes, and gas velocity. Analysis confirms that velocity difference (due to two-phase momentum exchange) dominates the formation of large-scale vortices from the southern and northern poles, corresponding to Kelvin–Helmholtz instability. Moreover, the influences of effective Atwood number on the evolutions of cloud morphology, vorticity, and gas velocity are evaluated. Results show that higher droplet concentration results in wider droplet dispersion range due to larger vortices.

Parametric study of hydrogen concentration on detonation initiation by shock focusing

Previous studies indicated that shock focusing is an effective way leading to detonation initiation. Hydrogen concentration as an operating condition is crucial to detonation initiation when the combustible gas is a mixture of hydrogen-air. To discuss the effect of hydrogen concentration, simulations of initiation by shock focusing with different hydrogen concentrations are performed. This paper provides an analysis of initiation by fuel in different amounts (in rich, stoichiometric, and lean). The initiation behaviors of shock focusing with different hydrogen concentrations (range from 20 vol% to 60 vol%) are discussed. The results show that high hydrogen concentration on initiation is significantly effective in accelerating the attenuation of overdriven detonation, which is conducive to initiating a quick and stable detonation initiation. An examination also shows that detonation failure is more likely caused by lean fuel mixtures. As to rich and stoichiometric fuel, there is the same physical mechanism for detonation initiation.

Numerical investigation of laser-driven shock interaction with a deformable particle

A laser-driven shock propagating through an isolated particle embedded in a plastic (CH) target was studied using the radiation-hydrodynamic code FLASH. Preliminary simulations using IONMIX equations of state (EOS) showed significant differences in the shock Hugoniot of aluminum compared to experimental data in the low-pressure regime [O(10) GPa], resulting in higher streamwise compression and deformation of an aluminum particle. Hence, a simple modification to the ideal gas EOS was developed and employed to describe the target materials and examine the particle dynamics. The evolution of the pressure field demonstrated a complex wave interaction, resulting in a highly unsteady particle drag which featured two drag minima due to shock focusing at the rear end of the particle and rarefaction stretching due to laser shut-off. Although ∼30% lateral expansion and ∼25% streamwise compression were observed, the aluminum particle maintained considerable integrity without significant distortion. Additional simulations examined the particle response for a range of particle densities, sizes, and acoustic impedances. The results revealed that lighter particles such as aluminum gained significant momentum, reaching up to ∼96% of the shocked CH's speed, compared to ∼29% for the heavier tungsten particles. Despite the differences seen in the early stage of shock interaction, particles with varying acoustic impedances ultimately reached the same peak velocity. This identified particle-to-host density ratio is an important factor in determining the inviscid terminal velocity of the particle. In addition, the modified EOS model presented in this study could be used to approximate solid materials in hydrocodes that lack material strength models.

Numerical investigation on reacting shock-bubble interaction at a low Mach limit

We investigate the deflagration combustion in the reacting shock-bubble interaction at M = 1.34 using a novel adaptive mesh refinement combustion solver with comprehensive H2/O2 chemistry. The numerical results are compared with an experiment by Haehn et al [1]. The Richtmyer-Meshkov instability dominates the shock-bubble interaction, and the shock focusing in the heavy bubble induces ignition. By following the initial experimental setup published by Haehn et al [1]. and adopting the axisymmetric assumption, we successfully reproduce most of the flow features observed in the experiment both qualitatively and quantitatively, including the bubble morphology evolution and the corresponding chemiluminescence images. The fuel consumption rate is nonmonotonic because of unsteady flame propagation, and it also depends on interfacial instabilities. The deflagration waves increase transverse bubble diameter, mildly decrease the total vorticity, and promote mixing by more than 150% because of the thermal effects. The mixing promotion is approximately 88% related to the diffusivity and 12% related to other mechanisms after ignition. A new shock focusing mechanism is observed due to the secondary refracted shock. During shock focusing, Mach reflection occurs and transits from the bifurcated type to the single type. This transition causes two ignitions: the first occurs in the spiral hot spot entrained by the jet vortex, and the second arises from the hot spot caused by the triple point collision. After the second ignition, the newborn flame is a deflagration at the beginning but is unstable and tends to transit to a detonation as a consequence of shock-flame interactions. Nevertheless, the deflagration-to-detonation transition fails, and the stable combustion mode is deflagration.

Evolution mechanism of double-layer heavy gas column interface with sinusoidal disturbance induced by convergent shock wave

Based on Navier-Stokes equations, combining the fifth-order weighted essentially non-oscillatory scheme with the adaptive structured grid refinement technique, the interactions between converging shock and annular SF<sub>6</sub> layers with different initial perturbation amplitudes and thickness are numerically investigated. The evolution mechanism of shock structure and interface are revealed in detail, and the variations of the circulation, mixing rate and turbulent kinetic energy are quantitatively analyzed. The dynamic mode decomposition method is used to analyze the dynamic characteristics of the vorticity. The results show that in the case with large initial perturbation amplitude, the transmitted shock wave forms Mach reflection structures both inside and outside of the inner interface of SF<sub>6</sub> layer, and multiple shock focusing phenomena occur in the center. After the transmitted shock wave penetrates the outer interface, the circulation increases faster, and the “spike” and “bubble” structure on inner interface develop faster, so that the amplitude of the inner and outer interfaces and the gas mixing rate increase. As for the case with larger thickness of the gas layer, the phase of the transmitted shock wave changes inside the layer, which forms “bubble” at the crest of the inner interface and “spike” at the trough. When the thickness of the gas layer decreases, the crest of the inner interface does not move inside after being impacted, and “spike” and “bubble” are generated in the late stage. The dynamic modes show that the main structure of vorticity and the exchange of positive and negative vorticity on the main structure are determined by the modes with weak growth and low frequency, but the modes with weak growth and high frequency determine rapid exchange of positive and negative vorticity at the interface in the cases with weak coupling effect.

Effects of obstacle layout and blockage ratio on flame acceleration and DDT in hydrogen-air mixture in a channel with an array of obstacles

Numerical simulations were performed to study flame acceleration and deflagration-to-detonation transition (DDT) in hydrogen-air mixture in a channel with a two-dimensional array of cylindrical obstacles. A high-order numerical algorithm with adaptive mesh refinement was applied to solve reactive Navier-Stokes equations. The effect of obstacle layout was examined by considering three layouts at a fixed blockage ratio of 0.5: staggered, inline-concentrated, and inline-scattered. Three blockage ratios, 0.33, 0.5, and 0.67, were used for the case of staggered obstacles to explore the influence of blockage ratio. The results show that both obstacle layout and blockage ratio have significant effects on flame acceleration and DDT occurrence, although the basic mechanism of detonation initiation is consistent for all the cases involving shock focusing. In the staggered case, the head-on collisions of flame and pressure waves with obstacles greatly promote the growth of flame surface area and thus lead to the fastest flame acceleration and shortest detonation onset time. In the inline-concentrated case, flame propagates slower than that in the staggered case due to smaller flame surface area. However, compared to the zigzag path in the staggered case, the straight passages parallel to flame propagation direction in the inline-concentrated case are more conducive to producing strong shock focusing and thus result in the shortest DDT distance. In the inline-scattered case, the straight passage along the centerline of channel facilitates the early acceleration of flame, but it has the slowest flame propagation in lateral directions and thereby the longest DDT time and distance. For the staggered obstacles at different blockage ratios, flame acceleration rate increases with increasing blockage ratio. The occurrence of DDT is hindered by the most congested obstacles, because the shock focusing is insufficiently strong to initiate detonation after passing through the excessively narrow gaps.