ZND Detonation Research Articles

The detonation pressure measurement of lead azide based on PDV technology

Abstract In order to measure the detonation pressure of lead azide, a test method and device for the detonation pressure of lead azide was designed in this paper. Based on the PDV technology, the interface particle velocity tests of lead azide were carried out, and the heights of the charge were 1.5 mm, 2.0 mm and 4.0 mm respectively. Then, the interface particle velocity curves of lead azide with different heights were obtained by mediating the original data. Owing to the interface particle velocity variation process corresponding to the pressure distribution in its ZND detonation model, we can obtain the VM peak and CJ point of lead azide from interface particle velocity curve of 4.0 mm charge height. The VM peak and CJ point of lead azide is 1553±30 m/s and 1031 m/s, respectively. Finally, based on impedance matching formula, it can be obtained that the VN pressure is 25.097 GPa and the detonation pressure (CJ pressure) is 15.705 GPa, and the duration of the detonation reaction zone is about 49 ns.

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.

Collision enhancement in shocks and its implication on gas-phase detonations: A molecular dynamics and gas-kinetic theory study

Conventional assumption in gas-phase detonations, where shock compression is decoupled from chemical kinetics, predicates on the shock and triple point structures being treated as perfect discontinuities. However, the shock is a region of high translational nonequilibrium three to five mean free paths in thickness. In this study, we use molecular dynamics simulations to probe Ar and N2 shocks focusing on the collision statistics in the shock front. Translationally superheated molecules were identified, as suggested by Zeldovich (Dokl. Akad. Nauk 248 (1979) 349–351), which raise the collision temperature and potentially enhance chemical reaction rates within and ahead of the shock front. We evaluated this reaction rate enhancement effect on stoichiometric H2/O2 ZND detonation and found the effect to be negligible. The triple point region is observed to have a similar distribution of translationally superheated molecules. The temperature in the triple point region in Ar is substantially higher than that in N2; the difference could impact detonation and deflagration-to-detonation characteristics due to diluent differences.

Multi-scale modeling of shock wave propagation in energetic solid-state composites

We present a novel structural dynamics code for modeling shock and detonation waves in Polymer-Bonded Explosives (PBXs), which are crucial for conventional munitions and propulsion components. Our code uses a stable and efficient solution strategy based on a Taylor–Galerkin finite element (FE) discretization to accurately predict PBX behavior under extreme shock loading. To model the PBXs, we implement equations of state for the solid unreacted material and gaseous reaction products using a pressure mixture rule governed by pressure-based reaction rates. We verify the FE model using analytical solutions for SOD shock and ZND detonation models. In addition to the continuum model, we also introduce a first-order multi-scale model that uses a Taylor approach to compute macro-scale fluxes and properties from the underlying microstructural sub-problems using averaging schemes. Our numerical results demonstrate the effectiveness of our multi-scale model in accurately predicting pressure profiles and detonation velocities for microstructures with varying mass fractions. These findings have significant implications for microstructure design and highlight the importance of considering microstructural variability in PBX behavior. Overall, our structural dynamics code represents a significant step towards improving the understanding and design of PBXs under extreme shock loading conditions.

Performance analyses of detonation engine cogeneration cycles

AbstractAircraft engines such as gas turbines and detonation engines have very important attention by the researchers in the last decades. However, using detonation engines for producing electrical and heat power was not researched efficiently. In this study, gas turbine and pulse detonation engines cogeneration systems were analyzed and compared by using first and second laws of thermodynamics and exergy analysis method. Three different cycles, namely, basic gas turbine, Zeldovich–von Neumann–Döring (ZND) detonation engine and steam injected regenerative ZND detonation engine cogeneration systems were investigated. The performance analyses and the advantage of these three cycles were obtained and discussed. The performance analyses were done for different compression ratios (r), and the combustion outlet temperatures and pressures, exergy efficiencies, specific fuel consumption, electrical efficiency, exergy fuel consumption, electrical heat rates and other performance parameters of the three cycles were obtained and discussed. It is found that gas turbine cogeneration systems have some advantages and disadvantages in some conditions than ZND cycle. The steam injected regenerative ZND detonation engine cogeneration systems can compete with the Brayton cycle cogeneration systems.

Effect of mole weight ratio of reaction on propagation of cellular detonations

The propagation of two-dimensional cellular detonations is investigated numerically using a one-step reversible reaction model. The effect of the average mole weight ratio WB/WA of the product and reactant on the one-dimensional Zeldovich–von Neumann–Döring (ZND) detonation and cellular detonation behavior is analyzed in detail. Several interesting cellular detonation phenomena are observed in the numerical simulations. These can be divided into five categories according to the cell patterns of detonation, i.e., regular, relatively regular, irregular, half-cell propagating, and decoupled detonation. The results indicate that differences in cell size under different values of WB/WA modify the cellular detonation behavior. The ZND detonation parameters under various WB/WA values are studied and related to the cell size. The results show that the reaction zone length and maximum heat release rate are clearly influenced by WB/WA. Furthermore, for both ZND detonation and cellular detonation, the reaction zone length decreases as WB/WA increases, which effectively reduces the cell size. To elucidate the effects of the reaction zone length on cell size, thermoacoustic instability theory is introduced to investigate the acoustic perturbations in the reaction zone. This allows the correlation between the propagation frequency and cell number along the width of the duct to be determined. Correlation analysis indicates that the cell number has a strong linear dependence on the perturbation frequency.

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.

Natural gas versus methane: Ignition kinetics and detonation limit behavior in small tubes

Detonation properties of methane and natural gas were studied using ZND simulations and detonation limit experiments. The experiments were performed in two tube sizes, 32 mm and 6.4 mm in inner diameter over a range of initial pressures (between 3.4 kPa and 35 kPa) and with stoichiometric fuel-oxygen compositions. The fuels considered are high purity methane, high purity methane with dopant ozone, a real natural gas, and a family of natural gas surrogates. The natural gas surrogates were developed based on North American natural gas composition variations and designed to capture the expected mean and variance of fundamental combustion properties of natural gases. All natural gases tested in this work show a substantially smaller detonation induction length (about 40%) and lower detonation pressure limit (30% in terms of limiting pressure) than high purity methane. The ozonated methane at 3000 PPMv of ozone doping performed similarly to the natural gases. Overall, the results suggest that in methane-based mixtures, a smaller induction length correlates with a more predictable detonation behavior as evidenced by a lower detonation pressure limit. As such, natural gases are expected to have a wider operating range when used as a fuel for detonation-based engines. As importantly, induction length calculation results reveal that the variability in detonation and combustion behaviors resultant from composition variability is expected to be similar between natural gases and commercial methane. Finally, the results suggest that for safety-related studies, neat methane is a poor surrogate for studying natural gas explosions.

STUDY ON EVOLUTION MODEL OF GASEOUS DETONATION WAVE IN PERIODIC INHOMOGENEOUS MEDIUM

The initiation, steady propagation and failure mechanism of gaseous detonation wave in periodic inhomogeneous media are very complex, and many physical mechanisms are still unclear, which is an active topic in detonation physics. Numerical simulation of propagation of gaseous detonations in the inhomogeneous medium is studied by using the reactive Euler equations coupled with a two-step chemical reaction model. The inhomogeneity is generated by placing artificial temperature perturbations with different wavelengths and amplitudes. The influence of temperature disturbance with different wavelength and amplitude on the structure of wave front is analyzed. The results show that, the transition of ZND detonation to cellular detonation under artificial temperature disturbance is mainly controlled by two competitive factors: one is the intrinsic instability of detonation wave, the other is the wavelength and amplitude of artificial disturbance, the former is the internal factor, the latter is the external factor. The existence of artificial temperature disturbance delays the evolution of ZND detonation to cellular detonation by suppressing the development of shear wave, and the increase of internal instability can slow down this delay phenomenon. This shows that the artificial temperature disturbance can restrain the development of cell instability in a certain range, but it cannot stop the process. The discontinuity of temperature makes the detonation wave front more distorted, which leads to the existence of a weak triple-wave structure near the shear wave, which is, the artificial disturbance increases the inherent instability of detonation wave and changes the propagation mechanism of detonation wave front. The propagation of detonation and the instability of detonation are restrained by the artificial temperature disturbance with large amplitude. The formation of detonation front cellular structure depends on the artificial temperature disturbance and its own instability.

Inhibition of hydrogen–oxygen/air gaseous detonations using CF3I, H2O, and CO2

The ignition of hydrogen-air mixtures can cause intense explosions. To ensure the safe utilization of hydrogen fuel and prevent catastrophic explosion accidents, the inhibiting effect of flame inhibitors must be understood since they have important consequences for hazard analyses. In the present study, the detonability of hydrogen mixtures diluted with CF3I, H2O, CO2, and N2 is investigated using numerical computations. The inhibiting effect of chemically active (CF3I, H2O, and CO2) and chemically inert (N2) diluents on the chemical length and time scales of a ZND detonation structure was studied using a detailed chemical kinetic mechanism for hydrogen oxidation. The inhibition efficiency of a halogenated compound, CF3I, towards quenching of hydrogen-air/oxygen gaseous detonations was also studied. As an additive, CF3I was found to promote detonation at lower concentrations. However, at higher concentrations, CF3I suppresses gaseous detonations by acting as a radical-scavenging agent. In the present study, a given retardant's effectiveness for suppressing a given detonation wave was evaluated for CF3I, H2O, CO2, and N2. The combined suppression effects of CF3I, H2O, and CO2 were also investigated. The efficacy of a composite inhibitor towards the quenching of a detonation wave was also evaluated and compared.

Unsteady propagation of detonation with multi-stage heat release

This work numerically studies the propagation characteristics of detonation waves with multi-stage heat releases (MSHR) for stoichiometric dimethyl ether/oxygen (DME/O2) mixtures with carbon dioxide (CO2) addition. Results show that detonation with MSHR is intrinsically unstable and will develop to a new mode. It is found that in the mixtures with mu lti-stage heat release the steady structure on the scales predicted by the ZND theory cannot exist and evolves into a detonation wave with much thinner structure through the particular paths via which the ZND detonation losses its stability. For different MSHR features induced by CO2 addition, two detonation development modes with double- and single-head structures are observed, with the former controlled by the merging of second- and third-stage heat release, while the latter triggered by the second-stage heat release with the fastest heat release rate.

Numerical Studies on Propagation Mechanisms of Gaseous Detonations in the Inhomogeneous Medium

Numerical simulation of propagation mechanisms of gaseous detonations in the inhomogeneous medium is studied by using the reactive Euler equations coupled with a two-step chemical reaction model. The inhomogeneity is generated by placing artificial temperature perturbations with different wavelengths and amplitudes. The motivation is to investigate the effect of artificial perturbations on the evolution or amplification of cellular instability. The results show that, without artificial perturbations, a planar ZND detonation can evolve into a fully-developed cellular detonation after a distance because of the amplification of the cellular instability. With the artificial perturbations evolved in, at the early stage, the artificial perturbations control the transverse wave spacing by suppressing the amplification of the cellular instability. However, after a steady-state, the cellular instability starts to amplify itself again and eventually transits to a fully-developed cellular detonation. It is demonstrated that the presence of the artificial perturbations delays the formation of the cellular detonation, and the increase of instability factor can slow down this delay. It is also found that, if the wavelength of the artificial perturbations is close to the transverse wave spacing of the cellular detonation in the homogeneous medium, synchronization of these two factors occurs, and hence a cellular detonation with extremely regular cell pattern is immediately formed. The temperature discontinuity causes the front to be more turbulent with the presence of weak triple-wave structure locally besides the natural transverse waves. The artificial perturbations can increase the intrinsic instability, and hence changes the propagation mechanism of the detonation front. In contrast, large artificial perturbations could prohibit the propagation but reduce cellular instability. It is concluded that the competition of artificial perturbations with intrinsic detonation instability dominates the evolution of cellular structures of the detonation front.

StanShock: a gas-dynamic model for shock tube simulations with non-ideal effects and chemical kinetics

A high-order, quasi-one-dimensional, reacting, compressible flow solver is developed to simulate non-ideal effects and chemical kinetics in shock tube systems. To this end, physical models for the thermoviscous boundary-layer development, area variation, gas interfaces, and reaction chemistry are considered. The model is first verified through simulations of steady isentropic nozzle flow, multi-species Sod’s problem, laminar premixed flame, and ZND detonation test cases. Comparisons with experiments are made by examining end-wall pressure traces that are gathered from shock tube experiments designed to test the code’s capabilities. Subsequently, the solver is utilized for uncertainty quantification and design optimization of a driver insert. Both applications prove to be highly efficient, indicating the utility of the solver for the design of experiments in consideration of non-ideal gas-dynamic effects.

Experimental and numerical studies on detonation reflections over cylindrical convex surfaces

The detonation reflection over a cylindrical convex surface was investigated experimentally and numerically by focusing on the length-scale effect on the reflection process, such as the triple-point trajectory and the critical wedge angle at which a transition occurs from regular reflection to Mach reflection. The results show that the critical wall angle plots exhibit significant scatter because of the cellular properties of the detonation front. If the transverse spacing is large as compared to the radius of curvature, the scatter range extends. If the transverse spacing is small as compared to the radius of curvature, the scattering is dramatically reduced. The critical wall angle is found to mainly depend on the scaled length i.e., the radius of curvature (R) over the cell size λ (or the reaction zone thickness Δ). Moreover, the critical wall angle increases with the decrease in the detonation thickness or with the increase in the radius. As R/λ increases to approximately ten, the critical wall angle approaches a value calculated using the non-reactive two-shock theory for pseudo-steady flows. The numerical results reveal that the transition to Mach reflection occurs earlier in the case of a ZND detonation than in the case of an inert shock wave because of the higher sound speed due to the release of chemical heat.

Effect of graphite particle size and content on the formation mechanism of detonation polycrystalline diamond

The formation mechanism of detonation polycrystalline diamond (DPD) generated from the detonation of a mixed RDX/graphite explosive is investigated. It is found experimentally that the DPD conversion rate decreases with both the content and the particle size of the graphite. Moreover, the particle sizes of the generated DPD powder are analyzed, which shows that, with the decrease in the graphite particle size, the mean number diameter of DPD decreases, but the mean volume diameter increases. In addition, with the help of scanning electron microscopy, it is observed that the in situ phase change occurs in the graphite particles, by which the small particles combine to form numerous large DPD particles. Based on both the experimental data and the classical ZND detonation model, we divide such a DPD synthesis process into two stages: In the first stage, the in situ phase change from graphite to diamond is dominant, supplemented by some coalescence growth at high pressure and temperature, which is affected mainly by the detonation performance of the mixed explosive under consideration. In the second stage, the graphitization of DPD caused by the residual heat is dominant, which is affected mainly by the unloading rate of the particle temperature.

Numerical simulation of Mach reflection of cellular detonations

The Mach reflection of cellular detonation waves on a wedge is investigated numerically in an attempt to elucidate the effect of cellular instabilities on Mach reflection, the dependence of self-similarity on the thickness of a detonation wave, and the initial development of the Mach stem near the wedge apex. A two-step chain-branching reaction model is used to give a thermally neutral induction zone followed by a chemical reaction zone for the detonation wave. A sufficiently large distance of travel of the Mach stem is computed to observe the asymptotic behavior in the far field. Depending on the scale at which the Mach reflection process occurs, it is found that the Mach reflection of a cellular detonation behaves essentially in the same way as a planar ZND detonation wave. The cellular instabilities, however, cause the triple-point trajectory to fluctuate. The fluctuations are due to interactions of the triple point of the Mach stem with the transverse waves of cellular instabilities. In the vicinity of the wedge apex, the Mach reflection is found to be self-similar and corresponds to that of a shock wave of the same strength, since the Mach stem is highly overdriven initially. In the far field, the triple-point trajectory approaches a straight line, indicating that the Mach reflection becomes self-similar asymptotically. The distance of the approach to self-similarity is found to decrease rapidly with decreasing thickness of the detonation front.

The response of plates subjected to loading arising from the detonation of different shapes of plastic explosive

The response of circular steel plates subjected to loading arising from the detonation of plastic explosive PE4 was investigated experimentally. The shape of the explosive charge, the charge dimensions and the charge mass were varied during the experiments. Cylindrical, truncated cone and the inverted truncated cone shaped explosives were detonated in close proximity to fully clamped circular plates fixed to a ballistic pendulum. The impulse, for the detonation of a given charge mass, was found to be highest for the inverted truncated cone. However, the maximum permanent displacement of the circular plates was greatest for the truncated cone shape. An analytical approach, combining the ZND detonation model with the concept of effective mass of explosive, was developed to gain understanding of the shape and intensity of the shock wave resulting from the explosion. The distribution of the shock wave obtained from the analytical approach was used to explain some of the experimental observations.

Mach reflection of a ZND detonation wave

The Mach reflection of a ZND detonation wave on a wedge is investigated numerically. A two-step chain-branching reaction model is used giving a thermally neutral induction zone followed by a chemical reaction zone for the detonation wave. The presence of a finite reaction zone thickness renders the Mach reflection process non-self-similar. The variation of the height of the Mach stem with distance of propagation does not correspond to a straight curve from the wedge apex as governed by self-similar three-shock theory. However, the present results indicate that in the near field around the wedge apex, and in the far field where the reaction zone thickness is small compared to the distance of travel of the Mach stem, the behavior appears to be self-similar. This corresponds to the so-called frozen and equilibrium limit pointed out by Hornung and Sanderman for strong discontinuity shock waves and by Shepherd et al. for cellular detonations. The critical wedge angle for the transition from regular to Mach reflection is found to correspond to the value determined by self-similar three-shock theory, but not by reactive three-shock theory for a discontinuous detonation front.

Precursors in two-phase detonation: An elementary model for the channel effect

The paper is concerned with the channel effect: detonation-propelled shocks occurring in tubular charges. It is shown that some salient aspects of the phenomenon may be successfully reproduced within a simple one-dimensional model assuming the gas–solid system to be isothermal and the volume fraction of the solid phase to be small. Two modes of the channel effect, dependent on the level of the ignition pressure, are identified. Although the emerging detonations appear to be of the Chapman–Jouguet (CJ) type, their velocities are controlled by the system’s gasification kinetics rather than its thermodynamics. The structure of the emerging CJ detonation differs from that of conventional ZND detonation. There is no shock attached to the reaction zone. The precursor shock is the only shock in the event.

Numerical Simulation of Cellular Structure of Weak Detonation and Evaluation of Linear Stability Analysis Predictions

This paper investigates the development of cellular structures created by the propagation of a detonation wave in a gaseous mixture. Two dimensional reactive Euler equations with an idealized one-step Arrhenius type reaction model are solved using the PPM scheme coupled with the exact Riemann solver. The numerical flow solver simulates the evolution process of regular cellular structures of a weakly unstable detonation wave. The cellular structures are generated by two-dimensional sinusoidal perturbations imposed on a ZND detonation wave. The initial sinusoidal perturbation wavelengths are predicted from linear stability analysis. The objective of these calculations is to examine the validity of the linear stability analysis predictions on the final cell sizes of a weakly unstable detonation. We found that for a given mixture, there is not just a single detonation cell size related to the wavelength with maximum growth rate. Instead, depending on the initial perturbation wavelength, the cellular dynamics reaches a final equilibrium state with the corresponding final cell size that belongs to a specific band of unstable wavelengths predicted by the linear stability analysis. Indeed, it is not the magnitude of the perturbation growth rate, but the magnitude of its rate of change with respect to the wavelength that predicts the domain of this specific band and corresponding final cell sizes.