Methane–oxygen detonation characteristics at elevated pre-detonation pressures

The detonation characteristics of methane–oxygen mixtures at pre-detonation pressures of 101–1,013 kPa were investigated in a detonation tube. Both pure methane–oxygen mixtures and mixtures with argon dilution were explored. Measurements made include cell sizes via soot foil, wave speed via high speed ion probes / pressure transducers, and temperature / H₂O molar concentration profiles via 100 kHz absorption spectroscopy. Measured cell widths agreed with predicted cell widths based on a ZND length correlation. In addition, the power law fit of cell width with pre-detonation pressure agreed with previous data at less than 101 kPa. Measured detonation wave speeds agreed within 3% of Chapmen-Jouguet for all cases. H₂O molar density and temperature were successfully captured up to 507 kPa. However, above 507 kPa pre-detonation pressure, low signal to noise ratio and poor spectral fits at the extreme conditions of the von Neumann spike resulted in unacceptable uncertainty. These results provide a unique dataset to validate kinetics models and high-fidelity computation fluid dynamics codes for methane-oxygen detonations at elevated pre-detonation pressures relevant to rotating detonation rocket engines.     

Cellular pattern formation in detonation propagation

The relation between the soot track on smoked plate records and the frontal structure of gaseous detonations was experimentally studied to clarify the mechanism of cellular pattern formation by using combination images of high-speed schlieren pictures, self-emission images of the reaction front, and the smoked plate record. Several materials were tested as alternatives to soot particles of smoked foil technique to record detonation structure. The experimental results show that the triple point trajectory coincides with the soot track and that cellular cell-like patterns are obtained for CaCO₃ particles, fly ash, heat-sensitive paper, and pressure-sensitive paper. An asymmetrical cellular pattern in the smoked plate record is exhibited in the case of the pressure-sensitive paper, while a symmetrical pattern is observed for the other materials. This asymmetry is successfully explained by the temporal response of the pressure-sensitive paper from evaluation of time integration of pressure, namely impulse to time varying loading. Estimation of wall shear stress and tensile strength of agglomerated particles layer on the basis of an analogy to particle entrainment from fine powder layers shows the critical particle diameter for removal of particles. However, the shear stress is found to be not strong enough for removal of particles located in the triple point trajectory. Finally other additional mechanisms for local detachment of particles are discussed.     

Spinning detonation and velocity deficit in small diameter tubes

Detonation velocities and soot patterns of H₂/O₂ mixtures were measured in glass tubes of 3, 6 and 10 mm diameters at pressures ranging from 70 to 400 Torr and equivalence ratios of 0.5–1.5. It was confirmed that the transition from a multi-head to a spinning detonation occurred at the pressure where the cell size is equal to the length of circumference. At this transition pressure, the velocity was 95% of the C-J detonation. Stable spinning detonations were observed at wide range of initial pressures below the transition point. Detonation velocities were continuously decreasing with decreasing initial pressures in this pressure region. Spinning detonations with velocities down to 85% of the C-J detonation were observed. Those deficits in detonation velocities were well predicted by the modified ZND model with full detailed chemical kinetics. Heat and momentum losses were taking into account in this model. Validity of the modified ZND model to define the limit of detonation propagation was discussed.     

气相爆轰波数值模拟中化学反应模型研究

 基于改进的时 空守恒元解元算法对气相爆轰波数值模拟中3种常用化学反应模型(二步模型,基元反应模型和Sichel的二步模型)进行了考察。对平面爆轰波和具有胞格结构的爆轰波进行了数值模拟,并对数值结果进行了比较和讨论。结果表明3种化学反应模型得到的爆轰参数准确性有所差异,但得到的胞格结构均能和实验结果较好吻合。3种化学反应模型在爆轰波数值模拟中各有优缺点,应视具体问题决定使用哪种化学反应模型。     

Statistical analysis of detonation wave structure

Hydrocarbon fueled detonations are imaged in a narrow channel with simultaneous schlieren and broadband chemiluminescence at 5 MHz. Mixtures of stoichiometric methane and oxygen are diluted with various levels of nitrogen and argon to alter the detonation stability. Ethane is added in controlled amounts to methane, oxygen, nitrogen mixtures to simulate the effects of high-order hydrocarbons present in natural gas. Sixteen unique mixtures are characterized by performing statistical analysis on data extracted from the images. The leading shock front of the schlieren images is detected and the normal velocity is calculated at all points along the front. Probability distribution functions of the lead shock speed are generated for all cases and the moments of distribution are computed. A strong correlation is found between mixture instability parameters and the variance and skewness of the probability distribution; mixtures with greater instability have larger skewness and variance. This suggests a quantitative alternative to soot foil analysis for experimentally characterizing the extent of detonation instability. The schlieren and chemiluminescence images are used to define an effective chemical length scale as the distance between the shock front and maximum intensity location along the chemiluminescence front. Joint probability distribution functions of shock speed and chemical length scale enable statistical characterization of coupling between the leading shock and following reaction zone. For more stable, argon dilute mixtures, it is found that the joint distributions follow the trend of the quasi-steady reaction zone. For unstable, nitrogen diluted mixtures, the distribution only follows the quasi-steady solution during high-speed portions of the front. The addition of ethane is shown to have a stabilizing effect on the detonation, consistent with computed instability parameters.     

Direct blast initiation of spherical gaseous detonations in highly argon diluted mixtures

In this study, direct initiation of spherical detonations in highly argon diluted mixtures is investigated. Direct initiation is achieved via a high voltage capacitor spark discharge and the critical energy is estimated from the analysis of the current output. Stoichiometric acetylene–oxygen mixtures highly diluted with 70% argon is used in the experiment. Previous investigations have suggested that detonations in mixtures that are highly diluted with argon have been shown to be “stable” in that the reaction zone is at least piecewise laminar described by the ZND model and cellular instabilities play a minor role on the detonation propagation. For the acetylene–oxygen mixture that is highly diluted with argon, the experimental results show that the critical energy where the detonation is “stable” is in good agreement with the Zel’dovich criterion of the cubic dependence on the ZND reaction length, which can be readily determined using the chemical kinetic data of the reaction. The experimental results are also compared with those estimated using Lee’s surface energy model where empirical data on detonation cell sizes are required. Good agreement is found between the experimental measurement and theoretical model prediction, where the breakdown of the 13λ relationship for critical tube diameter – and hence a different propagation and initiation mechanism – is elucidated in highly argon diluted mixtures and this appears to indicate that cellular instabilities do not have a prominent effect on the initiation process of a stable detonation.     

Cellular Cell Bifurcation of Cylindrical Detonations

Cellular cell pattern evolution of cylindrically-diverging detonations is numerically simulated successfully by solving two-dimensional Euler equations implemented with an improved two-step chemical kinetic model. From thesimulation, three cell bifurcation modes are observed during the evolution and referred to as concave front focusing, kinked and wrinkled wave front instability, and self-merging of cellular cells. Numerical research demonstrates that the wave front expansion resulted from detonation front diverging plays a major role in the cellular cell bifurcation, which can disturb the nonlinearlyself-sustained mechanism of detonations and finally lead to cell bifurcations.     

Detonability limits in thin annular channels

In this paper, detonability limits in two-dimensional annular channels are investigated. Since the channel heights are small in comparison to the tube diameter, curvature effects can be neglected and the annular channels can be considered to be essentially two-dimensional. Mixtures that are highly diluted with argon are used since previous investigations seem to indicate that detonations in such mixtures are “stable” in that cellular instabilities play minor roles on the propagation of the detonation. For stable detonations where the ZND structure is valid, boundary layer effects can be modeled as a flow divergence term in the conservation of mass equation following the pioneering work of Fay [J.A. Fay, Phys. Fluids 2(3) (1959) 283–289]. Expansion due to flow divergence in the reaction zone results in a velocity deficit. There exists a maximum deficit when an eigenvalue detonation velocity can no longer be found, which can be taken as the onset of the detonability limits. Experimentally, it was found that unlike “unstable” detonations, the detonability limits for “stable” detonations are well-defined. No unstable near-limit phenomena (e.g., galloping detonations) was observed. Good agreement is found between the theoretical predictions and the experimentally obtained velocity deficits and limits in the two channel heights of 2.2 and 6.9 mm for hydrogen–oxygen and acetylene–oxygen mixtures diluted with over 50% argon. It may be concluded that at least for these special mixtures where the detonation is “stable,” the failure mechanism is due to flow divergence caused by the negative displacement thickness of the boundary layer behind the leading shock front of the detonation wave.     

Numerical investigation on detonation cell evolution in a channel with area-changing cross section

The two-dimensional cellular detonation propagating in a channel with area- changing cross section was numerically simulated with the dispersion-controlled dissipative scheme and a detailed chemical reaction model. Effects of the flow expansion and compression on the cellular detonation cell were investigated to illustrate the mechanism of the transverse wave development and the cellular detonation cell evolution. By examining gas composition variations behind the leading shock, the chemical reaction rate, the reaction zone length, and thermodynamic parameters, two kinds of the abnormal detonation waves were identified. To explore their development mechanism, chemical reactions, reflected shocks and rarefaction waves were discussed, which interact with each other and affect the cellular detonation in different ways.     

Detonation propagation with velocity deficits in narrow channels

Propagation limits of detonations in narrow channels have been studied with a focus on velocity deficits and variation in cell widths. A channel was formed by a pair of metal plates of 1500 mm length which were inserted in a detonation tube of 50.5 mm inner diameter. Test gases were hydrogen–oxygen mixtures diluted with argon or nitrogen, which were selected as representatives of regular and irregular mixture systems. The velocity deficits predicted using the concept of negative boundary layer displacement thickness were compared to those obtained experimentally. From good agreement between the predicted and the experimental velocity deficits, the cell width enlarged in the channel was calculated using the induction zone length behind the decelerated leading shock front. Although this calculation underestimates the cell widths, the calculated cell widths were found to be well predicted when they were multiplied by an appropriate proportionality factor. It is found that for given mixtures, a combination of the calculated velocity deficit and the number of cells in a channel contributes to the prediction of propagation limits of detonations.     

Theory of gaseous detonations

The objective of the present paper is to review some developments that have occurred in detonation theory over the last ten years. They concern nonlinear dynamics of detonation fronts, namely patterns of pulsating and/or cellular fronts, selection of the cell size, dynamical self-quenching, direct (blast) or spontaneous initiation, and transition from deflagration to detonation. These phenomena are all well documented by experiments since the sixties but remained unexplained until recently. In the first part of the paper, the patterns of cellular detonations are described by an asymptotic solution to nonlinear hyperbolic equations (reactive Euler equations) in the form of unsteady (sometime chaotic) and multidimensional traveling-waves. In the second part, turning points of quasi-steady solutions are shown to correspond to critical conditions of fully unsteady problems, either for (direct or spontaneous) initiation or for spontaneous failure (self-quenching). Physical insights are tentatively presented rather than technical aspects. The challenge is to identify the physical mechanisms with their relevant parameters, and more specifically to explain how the length-scales involved in detonation dynamics are larger by two order of magnitude (at least) than the length-scale involved in the steady planar traveling-wave solution (detonation thickness).     

Multilevel detonation cell structures in methane-air mixtures

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

Effect of Cellular Instability on the Initiation of Cylindrical Detonations

The direct initiation of detonations in one-dimensional(1 D) and two-dimensional(2 D) cylindrical geometries is investigated through numerical simulations. In comparison of 1 D and 2 D simulations, it is found that cellular instability has a negative effect on the 2 D initiation and makes it more difficult to initiate a sustaining 2 D cylindrical detonation. This effect associates closely with the activation energy. For the lower activation energy,the 2 D initiation of cylindrical detonations can be achieved through a subcritical initiation way. With increasing the activation energy; the 2 D cylindrical detonation has increased difficulty in its initiation due to the presence of unreacted pockets behind the detonation front and usually requires rather larger source energy.     

Formation of double front detonations of a condensed-phase explosive with powdered aluminium

The performance characteristics of aluminised high explosive are considered by varying the aluminium (Al) mass fraction in a hybrid non-ideal detonation model. Since the time scales of the characteristic induction and combustion of high explosives and Al particles differ, the process of energy release behind the leading detonation wave front occurs over an extended period of time. Two cardinal observations are reported: a decrease in detonation velocity with an increase in Al mass fraction and a double front detonation (DFD) feature when anaerobic Al reaction occurs behind the front. In order to simulate the performance characteristics due to the varying Al mass fraction, the tetrahexamine tetranitramine (HMX) is considered as a base high explosive when formulating the multiphase conservation laws of mass, momentum, and energy exchanges between particles and HMX product gases. While experimental studies have been reported on the effect of Al mass fraction on both gas-phase and solid-phase detonations, the numerical investigations have been limited to only gas-phase detonation for the varying Al particles in the mixture. In the current study, a two-phase model is utilised for understanding the volumetric effects of Al mass fraction in condensed phase detonations. A series of unconfined and confined rate sticks are considered for characterising the performance of aluminised HMX with a maximum Al mass fraction of 50%. The simulated results are compared with the experimental data for 5–25% mass fractions, and the higher mass fraction behaviours are consistent with the experimental observations.     

Dynamics of Chapman-Jouguet pulsating detonations with Chain-Branching kinetics: Fickett’s analogue and Euler equations

The present study examines the spatiotemporal nonlinear dynamics of detonations over a wide range of reaction time scales away from the neutral stability region. This is addressed by one-dimensional numerical simulations with chain-branching kinetics. Fickett’s detonation analogue and Euler’s equations were used as evolution equations. A shock-fitting solver is used to reduce CPU time. Up to four thousand five hundred simulations have been carried out. Detailed bifurcation diagrams have been generated to explore the detonation dynamics. For long/intermediate reaction time scales, away from the neutral boundary, the traditional period-doubling cascade to chaos is seen. For square wave detonations, away from the neutral stability, almost periodic oscillations are recorded. This result might have implications for the existence of a characteristic length scale, the cell size, on typical cellular detonations which have a short reaction length.     

Cell structure and stability of detonations with a pressure-dependent chain-branching reaction rate model

We examine detonation waves with a four-step chain-branching reaction model that exhibits explosion limits close to the two lower limits of hydrogen–oxygen chemistry. The reaction model consists of a chain-initiation step and a chain-branching step, both temperature-dependent with Arrhenius kinetics, followed by two pressure-dependent termination steps. Increasing the chain-branching activation energy or the overdrive shortens the reaction length in the ZND wavelength and leads to more unstable detonations, according to multi-dimensional linear stability analysis. Corresponding numerical simulations show that detonations with weak chain-branching reactions have a wave structure similar to those with a single-step reaction; strong chain-branching detonations show distinct keystone features. Keystone regions are bounded by a discontinuity in reactivity across the shear layers emanating from the triple points at the intersection of the transverse waves and the main front. Especially in the strong case, chain-branching occurs within a thin front at the back side of the keystone figure, or immediately behind Mach stems.     

Studies on the valveless scheme to produce high-frequency detonations with different purge methods

Producing high-frequency detonations is an important topic for pulse detonations which has received considerable attentions. The valveless scheme has been verified to be able to obtain high-frequency detonations more than 100 Hz. This work has been conducted to investigate the possibility to achieve a higher detonation frequency and clarify the limits of stable operations preliminarily for the valveless scheme with different purge methods. Oxygen, ethylene, and nitrogen or liquid water are utilized as oxidizer, fuel, and purge medium in the experiments while two injection configurations are employed. The maximum detonation frequencies of 180 Hz and 330 Hz have been achieved in stable operations for two different injection configurations when nitrogen is used as the purge gas. The ceiling frequency for stable detonations is 300 Hz if nitrogen is replaced by liquid water, which indicates that water vapor is capable to create an efficient buffer zone to ensure stable operations. The results imply that the injection configuration also has a great impact on the ceiling stable detonation frequency. Three operating modes have been observed in this study, i.e., a stable detonation mode, an unstable detonation mode, and a deflagration mode. In the unstable mode, failure of detonation initiation occurs frequently and one interesting phenomenon is that the detonation frequency is reduced by half exactly when insufficient filling happens. The supply pressure ratios of oxidizer to fuel and purge to fuel are obtained for different operating modes when the purge method is changed. Furthermore, the equivalence ratios have been also studied for different operating modes which reveals that the range will change when different purge methods and injection configurations are employed. According to the equivalence ratio and the mass flow rates, an equivalent volume fraction of oxygen is defined and its range for the stable detonation mode is clarified.     

Detonation initiation from shock and material interface interactions in hydrogen-air mixtures

A numerical study was conducted to explore the mechanisms of detonation initiation in a stoichiometric hydrogen-air mixture resulting from the interaction between a Mach 2.8 shock and a perturbed material interface. The simulations used a high-order compressible numerical method for fluid dynamics with both detailed and simplified chemical-diffusive models. Three material interfaces were considered: no interface, a perturbed planar flame, and a perturbed helium interface. The case with no interface did not evolve into a detonation. The case with the flame produced a series of additional shock-flame and shock-shock interactions. The shock-shock interactions produced a series of contact surfaces and sliplines with increasing temperature. Hot spots eventually formed along these sliplines and a detonation was initiated shortly thereafter through a reactivity gradient mechanism. The overall process of detonation initiation was similar for both detailed and simplified chemical-diffusive models. Only the fine details, such as the precise time and location of the hot spots, were different. This indicates that simplified chemical-diffusive models are adequate to describe the initiation of detonations in the present configuration. The processes that ignited the detonation were also similar in the case where the flame was replaced with a helium interface. Helium has a similar acoustic impedance to the products and produced similar wave refraction patterns. Thus, the primary effect of the flame is to facilitate the shock-shock interactions that produce hot spots and initiate the detonation. The chemical energy released by the flame has a secondary influence.     

Numerical simulations of flame propagation and DDT in obstructed channels filled with hydrogen–air mixture

We study flame acceleration and deflagration-to-detonation transition (DDT) in channels with obstacles using 2D and 3D reactive Navier–Stokes numerical simulations. The energy release rate for the stoichiometric H₂–air mixture is modeled by a one-step Arrhenius kinetics. Computations show that at initial stages, the flame and flow acceleration is caused by thermal expansion of hot combustion products. At later stages, shock–flame interactions, Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instabilities, and flame–vortex interactions in obstacle wakes become responsible for the increase of the flame surface area, the energy-release rate, and, eventually, the shock strength. Computations performed for different channel widths d with the distance between obstacles d and the constant blockage ratio 0.5 reproduce the main regimes observed in experiments: choking flames, quasi-detonations, and detonations. For quasi-detonations, both the initial DDT and succeeding detonation reignitions occur when the Mach stem, created by the reflection of the leading shock from the bottom wall, collides with an obstacle. As the size of the system increases, the time to DDT and the distance to DDT increase linearly with d². We also observe an intermediate regime of fast flame propagation in which local detonations periodically appear behind the leading shock, but do not reach it.     

A review of direct numerical simulations of astrophysical detonations and their implications

Multi-dimensional direct numerical simulations (DNS) of astrophysical detonations in degenerate matter have revealed that the nuclear burning is typically characterized by cellular structure caused by transverse instabilities in the detonation front. Type Ia supernova modelers often use onedimensional DNS of detonations as inputs or constraints for their whole star simulations.While these one-dimensional studies are useful tools, the true nature of the detonation is multi-dimensional. The multi-dimensional structure of the burning influences the speed, stability, and the composition of the detonation and its burning products, and therefore, could have an impact on the spectra of Type Ia supernovae. Considerable effort has been expended modeling Type Ia supernovae at densities above 1×10⁷ g·cm^-3 where the complexities of turbulent burning dominate the flame propagation. However, most full star models turn the nuclear burning schemes off when the density falls below 1×10⁷ g·cm^-3 and distributed burning begins. The deflagration to detonation transition (DDT) is believed to occur at just these densities and consequently they are the densities important for studying the properties of the subsequent detonation. This work will review the status of DNS studies of detonations and their possible implications for Type Ia supernova models. It will cover the development of Detonation theory from the first simple Chapman–Jouguet (CJ) detonation models to the current models based on the time-dependent, compressible, reactive flow Euler equations of fluid dynamics.