Detonation Wave Research Articles

The effect of porous non-metallic balls on detonation propagation in hydrogen–oxygen mixtures

In this study, the influence of porous non-metallic balls on the dynamics of detonation propagation in hydrogen–oxygen mixtures is studied in stainless steel tubes with square cross-sections. The effect of the length and thickness of the balls is considered in detail. Four pressure transducers are used to record the detonation time-of-arrival, and the average velocity of detonation propagation is calculate. The smoked foil technique is performed to register the detonation cellular structures. The results indicate that increasing the filling length and thickness of the balls leads to a significant increase in velocity loss, critical pressure, and re-initiation distance during detonation propagation. Two propagation modes are observed near the critical pressure. In sub-critical mode, the detonation wave is attenuated and failed eventually, propagating to the end of the tube in the form of a low-speed deflagration wave. In super-critical mode, the detonation propagation can be promoted by inducing a vertical transverse wave generated by the detonation wave passing through a group of small balls. It is worth noting that the increase in filling thickness of the small balls leads to a greater velocity loss compared to the increase in filling length. However, an increase in the filling length will cause the detonation wave to undergo a longer and more sustained weakening process as it passes through the small balls, thereby resulting in a longer re-initiation distance and a lower average velocity over a short distance after re-initiation. By increasing the filling length of the small balls to 312 mm, the transition of the detonation wave from multi-head detonation to double-head detonation can be observed, and then successfully turns into stable detonation. However, when filling double-layer small balls, even in super-critical conditions, the attenuated detonation wave cannot achieve re-initiation over a short distance.

Pore collapse, shear bands, and hotspots using atomistics-consistent continuum models for RDX (1,3,5-trinitro-1,3,5-triazinane): Comparison with molecular dynamics calculations

Shock-induced energy localization is a crucial mechanism for determining shock sensitivity of energetic materials (EMs). Hotspots, i.e., localized areas of elevated temperature, arise when shocks interact with defects (cracks, pores, and interfaces) in the EM microstructure. The ignition and growth of hotspots in a shocked energetic material contribute to rapid chemical reactions that can couple with the passing shock wave, potentially leading to a self-sustained detonation wave. Predictive models for shock-to-detonation transition must correctly capture hotspot dynamics, which demands high-fidelity material models for meso-scale calculations. In this work, we deploy atomistics-guided material models for the energetic crystal RDX (1,3,5-trinitro-1,3,5-triazinane) and perform tandem continuum and all-atom molecular dynamics (MD) simulations. The computational setup for the continuum and MD simulations are nearly identical. The material models used for the calculations are derived from MD data, particularly the equations of state, rate-dependent Johnson–Cook strength model, and pressure-dependent shear modulus and melting temperature. We show that a modified Johnson–Cook model that accounts for shear-induced localization at the pore surface is necessary to represent well—relative to MD as the ground truth—the inelastic response of the crystal under a range of shock conditions. A head-to-head comparison of continuum and atomistic calculations across several metrics of pore collapse and energy deposition demonstrates that the continuum calculations are in good overall agreement with MD. Therefore, this work provides improved RDX material models to perform physically accurate meso-scale simulations, to enhance understanding of hot spot formation, and to use meso-scale hot spot data to inform macro-scale shock simulations.

Experimental investigation on propagation characteristics of rotating detonation wave fueled by diesel

Diesel fuel plays an indispensable role in the energy power sector. Detonation is a self-pressurizing combustion mode that can improve the utilization efficiency of diesel fuel. Through experiments, this paper explored the propagation characteristics of diesel/air RDWs within three different air-inlet slot width structures. A total of 24 high-pressure atomizing nozzles were evenly distributed circumferentially to inject diesel fuel into the combustor. The air, preheated by a heater, was injected into the combustor through the air-inlet slot. The results demonstrate the successful achievement of diesel/air rotating detonation under three different air-inlet slot width structures. As the width increases, the range of operating conditions for achieving detonation becomes more limited. As the air temperature rises, so does the detonation wave's propagation velocity, reaching up to 79 % of the theoretical CJ value. Both single-wave and two-wave collision modes were obtained in the experiments, with a constantly shifting collision point of the two-wave mode, forming the drift phenomenon. The establishment time for the detonation wave is comparatively short, ranging from 2.0 to 5.5 ms, and is minimally affected by the air-inject slot width and the total air temperature. The two-wave collision mode evolved from the single-wave form.

Propagation and stabilization properties of rotating detonation waves in a hollow combustion chamber with heated air inflow

The application of rotating detonation to conventional engine poses challenges such as high-temperature inflow conditions. In this study, experiments were conducted to discuss the propagation and stabilization properties of rotating detonation waves within a hollow rotating detonation combustor using pure heated air/ethylene as propellant. The temperature and equivalence ratio are varied to explore the boundary of detonative limits. The results show that the pressure of detonation waves is influenced by temperature fluctuations, whereas changes in air temperature have minimal impact on velocity losses. In addition to detonation, the deflagration zone is observed within the combustor. When the air temperature is increased, the deflagration zone expands gradually. The static temperature of air increases from 304 to 618 K, resulting in an increase in the area of the glowing zone from 17.7% to 60.0%. The expansion of the zone indicates a rise in deflagration percentage, and a stable single-wave mode is achieved mainly under fuel-rich conditions. The detonative equivalence ratio range is narrowed with increasing heated temperature at 484–618 K. Unstable propagation modes, characterized by sawtooth waves, are frequently observed at detonative lower limit, where the equivalence ratio is around 1.

The impact of film cooling on the heat release within a rotating detonation combustor

Rotating detonation combustors establish a detonation wave that continuously circulates inside a small annulus. The presence of the detonation wave and the downstream oblique shock within the small annulus coupled with high mass flow induces a high heat load to the combustor wall. Preliminary analysis shows that for higher thermal power, internal air cooling alone is not sufficient to remove the heat out of the walls to maintain them below the maximum temperature of the metal. A possible solution is to use film cooling to reduce the heat flux to the combustor walls. One issue, though, is that the introduction of film cooling provides additional air into the system that can influence the combustion process as well as providing a location for secondary combustion.This paper represents the first investigation to study the secondary implications on combustion of using film cooling in a rotating detonation combustor. The TU Berlin RDC architecture was modified with the introduction of 480 film cooling holes placed in the oblique shock region. High fidelity LES investigations were performed for different coolant plenum pressures to show the benefits of using film cooling. However, due to the presence of unburnt fuel in this post-detonation region, the coolant can result in additional combustion leading to an increase in temperature near the wall. One the one hand, these secondary reactions result in an increase of the overall heat release increasing combustion efficiency, however this also results in higher temperatures and reduced film cooling effectiveness. A simulation performed with nitrogen as a coolant enabled the effects of increased mixing caused by the ejection of coolant gases to be separated from the additional heat release. The simulation with nitrogen shows a reduction of 88% in the local heat release in the post detonation region resulting in similar performance as the uncooled case and significantly cooler walls.

Deflagration-to-detonation transition and detonation propagation in supersonic flows with hydrogen injection and downstream ignition

This study investigates the mechanisms of flame acceleration and deflagration-to-detonation transition (DDT) in supersonic flows using transverse hydrogen injection and downstream ignition. Utilizing the graphics processing unit accelerated adaptive mesh refinement approach, we examine the influence of downstream ignition jet pressure on DDT through high-resolution computational simulations. Our results indicate that the transverse injection of hydrogen into the supersonic mainstream generates strong turbulence and numerous vortices due to Kelvin–Helmholtz instability, enhancing fuel mixing efficiency along the flow but deviating from the ideal premixed state. Following the injection of the downstream ignition jet into the supersonic main flow, initial flame acceleration is less effective than in the premixed state due to the non-uniformity of the incoming flow. However, within the boundary layer, the flame remains stable, and the intense turbulence fosters shock–flame interactions. The convergence of multiple compression waves into a shock wave facilitates energy deposition, coupling with the flame to trigger local detonation via the reactive gradient mechanism. The detonation wave exhibits complex wavefront structures, including vertical and oblique fronts induced by boundary layer interactions. Ignition jet pressure significantly impacts the DDT process and detonation wave characteristics, reducing ignition time and affecting the detonation temperature, pressure, and propagation speed. This study provides valuable insights into the dynamics of flame acceleration and DDT in supersonic flows with non-uniform fuel distribution and downstream jet ignition. The findings highlight the critical role of ignition jet pressure in optimizing ignition and detonation processes, offering new perspectives for achieving low-energy, rapid detonation initiation within the tube.

Shock Propagation Through a Square Injector: Investigation into Rotating-Detonation Engine Injector Dynamics

The rotating detonation engine is perhaps the most promising means to realize pressure-gain combustion in modern engines. The physical processes underpinning the dynamics of the combustion wave are complex, and a lack of understanding of these processes represents a significant barrier to practical implementation of the technology. A significant simplification of the RDE is considered through an abstracted experimental setup. The detonation wave is replaced with a nonreacting shock generated by a shock tube, and the annulus is unwrapped into a single linear channel. Both simplifications make direct visualization of the problem via schlieren imaging tractable. Several performance metrics are used to relate the fluid-dynamic behavior of the shock–injector interaction to the performance of a theoretical rotating detonation engine. The first such metric is “recovery time,” based on the time taken for the injector to return to a fully flowing state after the passage of a detonation wave. The second such metric not only considers the mass flow through the injector exit but also accounts for potential backflow into the injector nozzle that may occur for sufficiently strong waves. Finally, a reactant mass-deficit metric is used to characterize the reduction in mass injection due to the interaction with the wave.

Analysis of waves dynamics in a rotating detonation combustor fueled by kerosene

The wave dynamics play a crucial role in the operation characteristics of the rotating detonation engine. We conducted numerical simulations of a rotating detonation combustor (RDC) using multicomponent reactive Navier–Stokes equations coupled with a discrete phases model. The RDC in this research employs a configuration with multiple coaxial injectors supplying oxygen-enriched air and kerosene spray at room temperature. To accurately identify and analyze waves within the RDC, we proposed a three-dimensional transient detonation wave detection method based on the combined parameters of normal Mach number and heat release rate in the flow field. Two typical wave modes, referred to as single-wave mode and counter-waves mode, are identified and then selected to conduct a detailed wave dynamics analysis. The general wave behavior is discussed, and velocity deficit is compared for these two wave modes. For the single-wave mode, intermittent micro-explosions are observed generating retonation waves periodically in the unburnt pockets behind the rotating detonation shock front. For the counter-waves mode, we analyzed the collision process of the two waves and the coupling/decoupling of the shock front with the detonative heat release zone, revealing the reason for significant velocity deficits in this wave mode. This research demonstrates that micro-explosions intermittently occur in the multiphase RDC in both single-wave and counter-waves modes and generate micro explosion shock waves periodically, which influence the complicated wave dynamics behavior.

Study on shock wave load characteristics from condensed phase explosive detonations in deep-water explosions

This study investigates shock wave load characteristics from condensed phase explosive detonations in deep-water environments using a high-order compressible multiphase solver. Spatial terms of the solver are discretized by fifth-order weighted essentially non-oscillatory reconstruction in characteristic space, while a third-order total variation diminishing Runge–Kutta method is adopted to deal with the temporal terms. The level-set method captures multiphase interfaces, while a programed burn model describes detonation wave generation. Numerical and experimental validations focus on shock waves in explosives interacting with water. Validations across shallow and deep-water conditions align numerical results with theoretical and experimental values. The solver examines shock wave characteristics across varied charge masses and water depths, revealing peak pressure deviations under identical conditions. The numerical simulation results indicate that the similarity of shock wave loads in underwater explosions is evident not only in peak pressures but also in the pressure–time history curves. Through extensive comparative analysis of results, it has been found that existing formulas for calculating shock wave positive pressure durations are not applicable to deep-water explosions. The research findings and analytical methods presented in this paper can serve as crucial references for further studies on the characteristics of shock wave loads in deep-water explosions.

Advancing instantaneous detonation prediction of condensed energetic materials based on high-order compressible multiphase fluid dynamics

The instantaneous detonation model (IDM) is widely used in simulating underwater explosions due to its efficiency and ability to ignore the detonation reaction process. In this study, we propose a new IDM to predict the fluid structure in the detonation zone of an RS211 explosive charge. This model is based on high-order solutions provided by the detonation shock dynamics model, where the spatial term is discretized using fifth-order WENO reconstruction in characteristic space and Lax–Friedrichs’s splitting and the temporal terms are discretized using a third-order TVD Runge–Kutta scheme. The interface motion is captured using the level-set method combined with MGFM, and a programmed burn model is provided to describe the generation and propagation of the detonation wave. The self-similarity of detonation wave propagation is validated, and the quantitative calculation formula of the instantaneous detonation model is obtained by averaging or curve fitting the dimensionless results. Consequently, the IDM of the RS211 charge is established using high-order polynomial approximations of the Taylor rarefaction zone and a constant static zone for 1D planar, cylindrical, and spherical RS211 charges. The application of the IDM involves direct mapping from the radial direction to the spatial structured grid for 1D planar, 2D cylindrical, and 3D spherical charges. Numerical results demonstrate that the IDM proposed in this paper shows good accuracy and high computational efficiency.

Numerical and experimental investigation on the operating characteristics of fan-shaped pulse detonation combustor

The internal flow channel of a turbine engine is typically annular. When circular pulse detonation combustors (PDCs) are installed in this channel, there is a problem with low section utilization rates. To solve this problem, a single-tube fan-shaped PDC test system was developed. The effects of ignition distance on the operating characteristics of the fan-shaped PDC using air and gasoline under different frequencies were studied through both experiment and 3-D numerical simulation. Numerical simulation was also used to investigate the formation and propagation characteristics of detonation waves. The results show that the fan-shaped PDC can operate stably at frequencies ranging from 5 to 25 Hz when the ignition distance is either 2.30 or 2.70 times the equivalent circle diameter from the thrust wall, and it is found to be better to ignite at a distance of 2.30 times the equivalent circle diameter. The blockage ratio of the lower arc surface is larger than that of the other surfaces. This results in more intense collision and reflection. A larger local high pressure area forms near the lower arc surface, which is conducive to the formation of detonation waves. However, the larger blockage ratio makes the flow loss larger, which weakens the intensity of the pressure waves near the lower arc surface. The detonation waves in the fan-shaped PDC travel closer to the upper arc surfaces.

Experimental study on the suppression of inlet blockage in rotating detonation combustor by porous-wall

The rotating detonation combustor (RDC) is renowned for its ability to provide substantial pressure gains. Nonetheless, during the stable operation of the RDC, the high-pressure rotating detonation wave (RDW) at the combustor inlet induces an increase in upstream chamber pressure, ultimately compromising engine stability and performance. To fully harness the performance advantages of the turbine-based continuous rotating detonation engine (TBCRDE) while maintaining engine stability, a porous-wall RDC has been developed to alleviate intake blockage and mitigate upstream chamber pressure rise. The operating modes, pressure rise characteristics, and performance parameters of both the porous-wall RDC and the reference configuration were systematically evaluated across varying air flow rates and nozzle designs. This analysis concentrated on the operational characteristics of the porous-wall RDC and its mechanisms for suppressing upstream chamber pressure rise. The findings reveal that the porous-wall RDC significantly extends the stable operating range and effectively reduces upstream chamber pressure rise by minimizing intake blockage. Specifically, the stable operating range is enhanced by 50 % at an outlet area ratio of 0.33, with stable rotating detonation combustion achieved at an outlet area ratio of 0.25. At an air flow rate of 1 kg/s and an outlet area ratio of 0.33, the chamber pressure rise is optimally suppressed, demonstrating a maximum reduction of approximately 16.4 %. The total pressure recovery coefficient of the combustor was analyzed, taking into account both intake loss and combustor pressure gain capabilities, and the propulsion performance of the two configurations was compared. The porous-wall RDC effectively reduces intake loss while slightly diminishing combustor pressure gain capability, resulting in a marginal increase in the total pressure recovery coefficient. Although this leads to a slight reduction in propulsion performance during chamber pressure rise suppression, the overall engine matching environment benefits from enhanced matching stability. Consequently, other engine components experience a reduced performance decline. Therefore, the implementation of a porous-wall structure is anticipated to improve the overall propulsion performance of the engine.

Numerical investigation on the interaction characteristics between the gaseous detonation wave and the water droplet

In this paper, the interaction characteristics between the gaseous detonation and the water droplet are numerically investigated, utilizing a modified compressible two-phase flow model coupling with detailed hydrogen-oxygen chemistry. Firstly, an analysis is conducted on the propagation behaviors of the cellular detonation obstructed by the droplet. It is found that the cellular detonation undergoes reflection, diffraction, local extinction, and re-ignition upon the obstruction, and these behaviors vary with the droplet relative positioning with multi-dimensional structures of the cellular detonation, particularly in terms of the extinction degree caused by the diffraction and the relative positioning of the re-ignition region. Further, the droplet deformation characteristics are detailly analyzed. It has been revealed that the deformation behavior of the shocked droplet under planar detonation is consistent with that under high-speed airflow. However, for the droplet shocked by the cellular detonation, several windward surface pits are induced due to impaction from transverse shocks and direct hitting of the triple-point. The emergence of these pits notably precedes the onset of surface instabilities caused by high-speed airflow erosion. Further investigation has revealed that post-detonation flow, through the entrainment effect of the central pit, progressively penetrates and segregates the droplet into upper and lower segments, and this penetrating effect heavily depends on the droplet relative positioning. Moreover, the side pit, whose presence is significantly determined by whether there is direct impaction of the triple-point on the droplet windward side, is crucial for the deformation around the droplet equator and the subsequent shedding of smaller droplets.

Mass Velocity Profiles for Non-Ideal Detonation of Mixtures of Nitromethane and Ammonium Perchlorate Overloaded with Aluminum. Measurements and Calculation

Earlier, by comparing the results of mathematical modeling with experimental data on the non-ideal detonation velocities of triple mixtures of nitromethane and ammonium perchlorate with aluminum excess, the rates of exothermic reactions and the consumption degree of components within the detonation wave reaction zone were determined. A quasi-one-dimensional model of steady detonation was used for calculations, in which all components have a common pressure and move with a common mass velocity, and exothermic conversion is carried out in three stages, which include decomposition of nitromethane and ammonium perchlorate and diffusion combustion of aluminum. To confirm the obtained results and the applicability of the relatively simple theoretical model, calculations of the mass velocity profile during detonation of one of the triple mixtures with 17% nitromethane have been carried out. The calculation results are in agreement with the measured mass velocity profile, concerning the shape of the profile, the amplitude and the rate of decrease of the mass velocity along the detonation reaction zone. A possible explanation of a “leaning” of the beginning portion of the mass velocity profile observed in experiments has been proposed, and an estimate of the rise time of the sensor signal is given, taking into account the calculated curvature of the shock front of the detonation wave.

Progress of Experimental Studies on Oblique Detonation Waves Induced by Hyper-Velocity Projectiles

Oblique detonation waves (ODWs) are hypersonic combustion phenomena induced by oblique shock waves. When applied to air-breathing engines, ODWs offer high thermal cycle efficiency, adaptability to a wide range of flight Mach numbers, and the advantage of a short combustion chamber, making them highly promising for hypersonic propulsion applications. Despite numerous numerical studies on the heat release and multi-wave flow mechanisms of ODWs, practical applications of oblique detonation engines (ODEs) remain limited due to several technical challenges. These challenges include generating the required high-velocity test environments, achieving effective fuel and oxidant mixing, and measuring the flow field structure in hyper-velocity and high-temperature flows. These limitations hinder the development of ODEs, underscoring the importance of experimental research, particularly for understanding the initiation and propagation mechanisms of ODWs. One of the primary experimental techniques involves inducing oblique detonation using high-velocity models. This method is extensively used to study the initiation process, shock structure, initiation criteria, and ODW propagation. It is advantageous because the state of the experimental mixture is controllable, and the model state can be precisely measured. This paper reviews studies on oblique detonation induced by hyper-velocity projectiles, presenting advances in experimental methods, detonation wave structures, unsteady processes, and initiation characteristics. Additionally, we discuss the deficiencies in existing studies, noting that the current measurement methods fall short of the requirements for observing the ODW initiation process, propagation process, and fine structure. The application of advanced combustion diagnostic techniques and the exploration of the relationship between initiation processes and criteria are crucial for advancing our understanding of ODW initiation and stabilization mechanisms. Finally, we summarize the current state of experimental facilities and measurement techniques, providing suggestions for future research on the measurement of shock waves and chemical reaction zones.

Space–time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation

The space–time adaptive ADER–DG finite element method with LST–DG predictor and a posteriori sub–cell ADER–WENO finite–volume limiting was used for simulation of multidimensional reacting flows with detonation waves. The presented numerical method does not use any ideas of splitting or fractional time steps methods. The modification of the LST–DG predictor has been developed, based on a local partition of the time step in cells in which strong reactivity of the medium is observed. This approach made it possible to obtain solutions to classical problems of flows with detonation waves and strong stiffness, without significantly decreasing the time step. The results obtained show the very high applicability and efficiency of using the ADER–DG–PN method with a posteriori sub–cell limiting for simulating reactive flows with detonation waves. The numerical solution shows the correct formation and propagation of ZND detonation waves. The structure of detonation waves is resolved by this numerical method with subcell resolution even on coarse spatial meshes. The smooth components of the numerical solution are correctly and very accurately reproduced by the numerical method. Non–physical artifacts of the numerical solution, typical for problems with detonation waves, such as the propagation of non–physical shock waves and weak detonation fronts ahead of the main detonation front, did not arise in the results obtained. The results of simulating rather complex problems associated with the propagation of detonation waves in significantly inhomogeneous domains are presented, which show that all the main features of detonation flows are correctly reproduced by this numerical method. It can be concluded that the space–time adaptive ADER–DG–PN method with LST–DG predictor and a posteriori sub–cell ADER–WENO finite–volume limiting is perfectly applicable to simulating fairly complex reacting flows with detonation waves.

Concerning the Parameterization of Geometric and Criticality Effects on Detonation Amplification

This study investigates the role of geometric effects and detonation criticality on the behavior of a detonation transition through an area expansion of finite length. Three reinitiation behaviors that result in an amplified pressure impulse were observed and are referred to as steady, spike, and endwall amplification. Steady amplification was characterized by an amplification event with a peak pressure impulse 2 times that of the inlet detonation, followed by a near-linear attenuation toward Chapman–Jouguet conditions. Spike amplification displayed a larger peak pressure amplification that was 3 to 5 times greater than the inlet detonation, followed by a rapid and nonlinear attenuation. Endwall behavior represents a Craven–Grieg deflagration to detonation transition scenario. These behaviors are shown to be factors of area expansion ratio and the degree to which the incoming detonation is subcrtical. A decoupling parameter, Ψd, was devised to combine these effects into a single correlation metric. The finite length of the expansion chamber also plays a role in the reinitiation behavior as observed by the endwall reinitiation behavior. A critical chamber length parameter was devised to explain this behavior and then theorized to have a relationship to Ψd with this being explored theoretically and with the limited data set available.

Modeling of nonequilibrium effects in a compressible plasma based on the lattice Boltzmann method

A magnetohydrodynamic lattice Boltzmann method (MHD-LBM) model for a 2D compressible plasma based on the finite volume scheme is established. The double distribution D2Q17 discrete velocities are used to simulate the fluid field. The hyperbolic Maxwell equations, which satisfy the elliptic constraints of Maxwell's equations and the constraint of charge conservation, are used to simulate the electromagnetic field. The flow field and electromagnetic field are coupled to simulate a compressible plasma through the electromagnetic force and magnetic induction equations. Four typical cases, the Taylor vortex flow, strong blast, Orszag–Tang vortex, and one-dimensional Riemann problems, are simulated to validate the MHD-LBM model for a compressible plasma. It is found that shock waves widely exist in a compressible plasma, and strong nonequilibrium effects exist around each shock wave. The quantitative simulation for the Brio–Wu problem demonstrates that this model can easily obtain the physical characteristics of nonequilibrium effects at sharp interfaces (shock waves and detonation waves). The magnetic fields can affect the magnitudes to which the system deviates from its equilibrium state. The viscosity can increase the magnitudes to which the system deviates from its equilibrium state. Compared with existing compressible MHD, these results for nonequilibrium effects can provide mesoscopic physical insights into the flow mechanism of a shock wave in a supersonic plasma.

Overlapping effect of detonation driving during multi-point initiation

Employing multi-point initiation in warhead structures produces a detonation wave aiming warhead. Numerous studies have concentrated on enhancing the velocity and analyzing its distribution in this type of warhead. Researchers have developed formulas for the velocity distribution of asymmetrically one-line initiated warheads; however, a reliable and complete calculation method for the velocity distribution in asymmetrically two-line initiated warheads is yet to be established. A new idea is proposed and verified in this work: the velocity distribution for the asymmetric two-line initiation can be derived from that of the one-line initiation. Initial efforts include conducting experimentally verified numerical modeling to examine the propagation and interaction of detonation waves in asymmetrically two-line initiated warheads. Subsequently, using the principle of independent propagation, a model is formulated to use the velocity distribution from asymmetric one-line initiation to predict that of asymmetric two-line initiations. Finally, arena tests are performed to corroborate the overlapping model. This research can provide valuable insights for lethality assessment, protection design, and security analysis.

Stereoscopic cells of three-dimensional detonation waves propagating in square ducts

The present study delves into the examination of the stereoscopic cells and wavefront structures characterizing the propagation of three-dimensional detonation waves within square ducts. Leveraging numerical solutions derived from three-dimensional reactive Euler equations, incorporating an induction-exothermic reaction kinetic model, this work reveals the distinct classification of three modes of detonation waves based on the direction of propagation and the phase characteristics of transverse shock waves on the wavefront. This paper delineates the presence of two different types of phenomena: duct wall slapping waves due to shock–wall collisions and internal slapping waves resulting from shock interactions. Furthermore, this investigation exposes the existence of two distinct types of triple-wave lines on the wavefront: the first comprising a strong Mach disk, a weak Mach disk, and a transverse shock wave; the second characterized by a weak Mach disk, an incident shock wave, and a transverse shock wave. Notably, the pressure behind the first type of triple-wave line is observed to be the highest. It elucidates the transition from two- to three-dimensional detonation waves, revealing that the prevalence of transverse shock waves on the wavefront in the rectangular and diagonal modes is twofold and quadruple, respectively, when compared to their two-dimensional counterparts within identical ducts/channels.