Numerical simulations of the cellular structure of detonations in liquid nitromethane—regularity of the cell structure

The detailed structure of planar detonation waves in liquid nitromethane was studied using time-dependent two-dimensional numerical simulations. The walls are assumed to confine heavily the liquid explosive and boundary layer effects are neglected. The solution thus simulates the detonation structure near the center of a wide channel. Chemical decomposition of nitromethane is described by a two-step model composed of an induction time followed by energy release. A simplified equation of state based on the Walsh and Christian technique for condensed phases and the BKW equation of state for gas phases us used. When mixtures of both phases are present, pressure and temperature equilibrium between them is assumed. The simulations show a cellular pattern traced by a system of triple points dividing the detonation front into sections. However, a substructure of weaker triple points also traces out a nonuniform pattern within the main pattern, resulting in an irregular cellular structure. A correlation exists between the regularity of the cellular pattern and both the curvature of the front and the change in induction zone thickness at the triple points. If the induction time is a stronger function of temperature, the weaker triple points disappear and a more regular structure is produced. When the structures are regular, the detonation front is more curved and there is a larger change in induction zone thickness at the triple points. However, the large change in induction zone thickness also leads to the formation of unburned pockets that eventually disturb the symmetry and uniformity of the structure. We conclude that the regularity of the cellular pattern is strongly influenced by the temperature-dependence of the induction time.     

Detonation propagation in narrow gaps with various configurations

In general all detonation waves have cellular structure formed by the trajectory of the triple points.This paperaims to investigate experimentally the propagation of detonation in narrow gaps for hydrogen-oxygen-argonmixtures in terms of various gap heights and gap widths.The gap of total length 1500 mm was constructed bythree pair of stainless plates,each of them was 500 mm in length,which were inserted in a detonation tube.Thegap heights were varied from 1.2 mm to 3.0 mm while the gap widths were varied from 10 mm to 40 mm.Variousargon dilution rates were tested in the present experiments to change the size of cellular structure.Attempts havebeen made by means of reaction front velocity,shock front velocity,and smoked foil to record variations of cel-lular structure inside the gaps.A combination probe composed of a pressure and an ion probe detected the arrivalof the shock and the reaction front individually at one measurement point.Experimental results show that thenumber of the triple points contained in detonation front decreases with decrease in the gap heights and gapwidths,which lead to larger cellular structures.For mixtures with low detonability,cell size is affected by a cer-tain gap width although conversely cell size is almost independent of gap width.From the present result it wasfound that detonation propagation inside the gaps is strongly governed by the gap height and effects of gap widthis dependent on detonability of mixtures.     

Diffusion and hydrodynamic instabilities in gaseous detonations

To clarify the role played by diffusion in detonation structure, two-dimensional numerical simulations are performed by solving the Navier–Stokes equations and considering the single step Arrhenius kinetic as reaction model. The effect of diffusion on the generation of vortices produced by hydrodynamic instabilities (Richtmyer–Meshkov (RM) and Kelvin Helmholtz (KH) instabilities) is investigated. Mixtures with both low and high activation energies, characterized by their regular and irregular detonation structures, are considered. The computations are performed with resolutions ranging from 25 to 10³ cells per half reaction length of the ZND structure. Resolution studies of the Navier–Stokes solution for irregular detonations in moderate activation energy mixtures shows that to capture a proper structure, to be at least in qualitative agreement with experimental observations, resolution more that 300 cells per half reaction length is required. However, in mixtures with low activation energy a resolution of 25 cells per half reaction length gives a reasonable physical structure of the detonation. Results provided by very high resolution for irregular structure detonations reveal that the major effect of diffusion occurs at shear layers and unburned pockets boundaries. Diffusion suppresses the small-scale vortices produced by KH instabilities and decreases the turbulent mixing rate of burned and partly burned gases at shear layers. However, behind the shock front, where less concentration of small-scale vortices exist, the diffusion of heat and mass from neighboring hot regions of burned material to the unreacted gases increases the burning rate of the un-reacted pockets. Comparison of the structure obtained by solving the Euler equations with the solution of the Navier–Stokes equations shows that, the strength of the shock front in Navier–Stokes solution is higher than that in Euler solution. Due to the absence of hydrodynamic instabilities behind the main front of regular structure detonations, the results obtained by solving the Euler equations and Navier–Stokes equations are similar for detonations with regular structure even in high resolution simulations.     

The influence of the cellular instability on lead shock evolution in weakly unstable detonation

The evolution of the normal detonation shock velocity (D_n) with local shock curvature (κ) is experimentally and numerically examined along entire evolving fronts of a weakly unstable cellular detonation cycle with the intention of extending the understanding of cellular evolution dynamics. As expected, a single velocity–curvature relation is not recovered due to the unsteady evolution of the cell. However, geometric features of the D_n–κ evolution during a cell cycle reveal some new details of the mechanisms driving cellular detonation. On the cell centerline, the local shock velocity and curvature monotonically decrease throughout the cellular cycle. Off centerline, a larger range of wavefront curvature was exhibited in expanding cells as compared to shrinking ones, indicating that most curvature variation in a detonation cell occurs near the Mach stem. In normal shock velocity–curvature space, the cell dynamics can be mapped to three features that are characteristic of (feature 1) a detonation with a spatially short reaction zone, (feature 2) a transitional regime of shock and reaction zone decoupling, and (feature 3) a diffracting inert blast wave. New, growing cells predominately exhibited features 1 and 2, while decaying cells only exhibited feature 3. The portions of all profiles with normal velocities below the Chapman–Jouguet velocity were characteristic of inert blast propagation, indicating the possibility that exceeding this velocity may be a necessary condition for the existence of shock and reaction zone coupling. In this inert blast regime, D_n and κ vary spatially across the wave front so each segment is not geometrically cylindrical, but when accumulated, the D_n–κ data map out a straight line, indicating elements of self-similar flow for each stage in the cell cycle.     

Direct observations of reaction zone structure in propagating detonations

We report experimental observations of the reaction zone structure of self-sustaining, cellular detonations propagating near the Chapman-Jouguet state in hydrogen-oxygen-argon/nitrogen mixtures. Two-dimensional cross sections perpendicular to the propagation direction were imaged using the technique of planar laser induced fluorescence (PLIF) and, in some cases, compared to simultaneously acquired schlieren images. Images are obtained which clearly show the nature of the disturbances in an intermediate chemical species (OH) created by the variations in the strength of the leading shock front associated with the transverse wave instability of a propagating detonation. The images are compared to 2-D, unsteady simulations with a reduced model of the chemical reaction processes in the hydrogen-oxygen-argon system. We interpret the experimental and numerical images using simple models of the detonation front structure based on the “weak” version of the flow near the triple point or intersection of three shock waves, two of which make up the shock front and the third corresponding to the wave propagating transversely to the front. Both the unsteady simulations and the triple point calculations are consistent with the creation of keystone-shaped regions of low reactivity behind the incident shock near the end of the oscillation cycle within the “cell.”     

Detonation cellular structure in NO2/N2O4-fuel gaseous mixtures

Experimental and numerical studies of the detonation in NO₂-N₂O₄/fuel (H₂, CH₄, and C₂H₆) gaseous mixtures show that for equivalence ratio Φ>0.8-1, (1) the detonation has a double cellular structure, the ratio between the cell size of each net being at least one order of magnitude; (2) inside the detonation reaction zone the chemical energy is released in two successive exothermic steps. Their chemical induction lengths, defined between the leading shock front and each local maximum heat release rate associated with each step, differ by at least one order of magnitude. The chemical reaction NO₂ + H → NO + OH is mainly responsible for the first exothermic step (fast kinetics), NO being the oxidizer on the second one (slow kinetics). Existence of correlations between calculated induction lengths and corresponding cell sizes strengthen the assumption that the cellular structure originates from local strong gradients of chemical heat release inside the detonation reaction zone.     

Detonation diffraction in gases

We have experimentally investigated detonation diffraction out of a round tube into an unconfined half-space. The focus of our study is examining how the extent of detonation cellular instability influences the quantitative and qualitative features of diffraction. Detailed quantitative and qualitative measurements were obtained through simultaneous schlieren imaging, multiple-exposure chemiluminescence imaging, and planar laser-induced fluorescence imaging of OH molecules. Two types of stoichiometric mixtures, highly diluted H₂-O₂-Ar and H₂-N₂O, were studied in the sub-critical, critical and super-critical regime. These mixture types represent extreme cases in the classification of cellular instability with highly diluted H₂-O₂-Ar mixtures having very regular instability structures and H₂-N₂O having very irregular instability structures. The most striking differences between the mixtures occur in the sub-critical and critical regimes, for which the detonation fails to transition into the unconfined half-space. For the H₂-O₂-Ar mixture, the velocity on the center line was found to decay significantly slower than for the H₂-N₂O mixture. In case of the H₂-O₂-Ar mixture, it was evident from simultaneous schlieren-fluorescence images that the reaction front was coupled to the lead shock front up to 2.3 tube diameters from the exit plane. For the H₂-N₂O mixture, the reaction front velocity decreased to 60% of the corresponding Chapman-Jouguet value at 1.1 tube diameters from the tube exit plane. A geometric acoustic model showed that the observed differences in failure patterns are not caused by the differences in thermodynamic properties of the two mixtures but is linked to the larger effective activation energy and critical decay time in the H₂-N₂O mixture as compared to the H₂-O₂-Ar mixture. The re-initiation events appear similar for the two mixtures and are a consequence of local fluctuations at random locations within the region between the lead shock and decoupled reaction zone, resulting in strong transverse detonations sweeping through shocked but largely unreacted gas.     

双点激光点火直接起爆的数值模拟

针对双点激光点火直接起爆过程中爆轰波的形成、发展和传播问题,采用高精度数值模拟方法求解带化学反应的二维欧拉方程组,研究了不同环境压力情况对流场结构与波系变化的影响.结果表明,环境压力会影响激波强度与爆轰波的传播速度,是决定双点激光点火形成的火核在碰撞过程中能否实现爆轰并维持爆轰波传播的重要因素,利用双激光点相互作用形成...     

On the normal detonation shock velocity-curvature relationship for materials with large activation energy

We derive the normal detonation shock velocity-curvature relation for a near-Chapman-Jouguet detonation, for an explosive material with Arrhenius kinetics and a large activation energy. Large activation energy asymptotics are used to develop an explicit exponential formula relating the shock curvature κ to the normal detonation shock speed, D_n. In this case, the D_n-κ relation is multivalued and has a turning point with a critical curvature κ_cr such that for κ > κ_cr, the possibility of detonation extinction arises. The asymptotic formula is in excellent agreement with the exact solution found by a numerical shooting procedure.     

Numerical study of acoustic coupling in spinning detonation propagating in a circular tube

Spinning detonations propagating in a circular tube were numerically investigated with a two-step reaction model by Korobeinikov et al. The time evolutions of the simulation results were utilized to reveal the propagation behavior of single-headed spinning detonation. Three distinct propagation modes, steady, unstable, and pulsating modes, are observed in a circular tube. The track angles on a wall were numerically reproduced with various initial pressures and diameters, and the simulated track angles of steady and unstable modes showed good agreement with those of the previous reports. In the case of steady mode, transverse detonation always couples with an acoustic wave at the contact surface of burned and unburned gas and maintains stable rotation without changing the detonation front structure. The detonation velocity maintains almost a CJ value. We analyze the effect of acoustic coupling in the radial direction using the acoustic theory and the extent of Mach leg. Acoustic theory states that in the radial direction transverse wave and Mach leg can rotate in the circumferential direction when Mach number of unburned gas behind the incident shock wave in the transverse detonation attached coordinate is larger than 1.841. Unstable mode shows periodical change in the shock front structure and repeats decoupling and coupling with transverse detonation and acoustic wave. Spinning detonation maintains its propagation with periodic generation of sub-transverse detonation (new reaction front at transverse wave). Corresponding to its cycle, whisker is periodically generated, and complex Mach interaction periodically appears at shock front. Its velocity history shows the fluctuation whose behavior agrees well with that of rapid fluctuation mode by Lee et al. In the case of pulsating mode, as acoustic coupling between transverse detonation and acoustic wave is not satisfied, shock structure of spinning detonation is disturbed, which causes failure of spinning detonation.     

Computational study of three-dimensional gaseous detonation structures

In this article we present a detailed numerical study of three-dimensional structures in gaseous detonations, using a parallelized, unsplit, shock-capturing algorithm. The computational domain consisted of a rectangular tube with periodic conditions on its lateral boundaries. A slightly perturbed ZND profile has been used as initial condition. Previous experimental studies in rectangular shock tubes suggest that there are two basic types of detonation structures: rectangular and diagonal ones. Rectangular structures are characterized by triple lines along the front that are parallel to the walls of the flow domain and by the presence of slapping waves on the walls. On the other hand, diagonal structures are characterized by diagonal triple lines and the absence of slapping waves on the walls. Both structures have been numerically reproduced in our study by suitably perturbing the initial conditions. All the important features of the flow fields that have been experimentally observed are reproduced in our simulations. Finally, an analysis of the geometric similarities between the two types of structures is also presented herein.     

Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube

In this paper, an experimental study on the near detonation limits for propane-hydrogen-oxygen is performed. Three mixtures (i.e., 8H₂–C₃H₈–9O₂, 4H₂–C₃H₈–7O₂ and 12H₂–C₃H₈–11O₂) are tested in a rectangular tube (52 mm × 32 mm). Photodiodes with regular intervals are mounted on the tube wall to measure the time of arrival of detonation waves, from which the detonation velocity is determined. Smoked foils are inserted into the tube to obtain the detonation cell pattern. The results indicate that well within the detonation limits, the detonation can propagate at a steady velocity. By reducing the initial pressure, the detonation velocity decreases gradually. Subsequently, the detonation fails as the initial pressure is below a critical pressure. The critical pressures for 8H₂–C₃H₈–9O₂, 4H₂–C₃H₈–7O₂ and 12H₂–C₃H₈–11O₂ mixtures are 4 kPa, 5 kPa and 6 kPa, and the corresponding detonation velocity deficits are 10%, 9%, 10%, respectively. The cellular detonation structures show that the cell size decreases with the decrease of the hydrogen concentration, and the cell structures are very irregular near the detonation limits.     

Observations of the cellular structure of fuel–air detonations

Detonation cell widths, which provide a measure of detonability of a mixture, were measured for hydrocarbon–air and hydrogen–air–diluent mixtures. Results were obtained from a 0.43-m-diameter, 13.1-m-long heated detonation tube with an initial pressure of 101 kPa and an initial temperature between 25 and 100 °C. The cell widths of simple cyclic hydrocarbons are somewhat smaller than those of comparable straight-chain alkanes. Cyclic hydrocarbons tested generally had similar cell sizes despite differences in degree of bond saturation, bond strain energy, oxygen substitution, and chemical structure. There was a significant reduction in the cell width of octane, a straight-chain alkane, when it was mixed with small quantities of hexyl nitrate. The effect of a diluent, such as steam and carbon dioxide, on the cell width of a hydrogen–air mixture is shown over a wide range of mixture stoichiometries. The data illustrate the effects of initial temperature and pressure on the cell width when compared to previous studies. Not only is carbon dioxide more effective than steam at increasing the mixture cell width, but also its effectiveness increases relative to that of steam with increasing concentrations. The detonability limits, which are dependent on the facility geometry and type of initiator used in this study, were measured for fuel-lean and fuel-rich hydrogen–air mixtures and stoichiometric hydrogen–air mixtures diluted with steam. The detonability limits are nominally at the flammability limits for hydrogen–air mixtures. The subcellular structure within a fuel-lean hydrogen–air detonation cell was recorded using a sooted foil. The uniform fine structure of the self-sustained transverse wave and the irregular structure of the overdriven lead shock wave are shown at the triple point path that marks the boundary between detonation cells.     

On the detonation propagation behavior in hydrogen-oxygen mixture under the effect of spiral obstacles

Detonation propagation velocity behavior and cellular structure of stoichiometric hydrogen-oxygen mixture in spiral obstacles with four roughness (ξ = 0.133, 0.231, 0.4, 0.625) are systematically examined, at the conditions outside-, near- and within the propagation limits. The experimental results indicate that, at p₀ = 10 kPa (outside the limits), spirals with roughness smaller than 0.4 facilitate the initiation of detonation, but ξ = 0.625 spiral causes the detonation quench earlier than that in smooth tube without spiral, and suggests it has prohibiting effect on the detonation propagation. At p₀ = 12 kPa (near the detonation limits), spirals with ξ = 0.133 and 0.231 extend the detonation limits and therefore they have the facilitating effect on the detonation propagation, but this positive effect is not obvious in the spiral with larger roughness (i.e., ξ = 0.4 and 0.625). As the initial pressure is higher than 15 kPa, under such condition detonations are well within the limits, the dual effects of promoting and prohibiting of the spiral on the detonation propagation are more obvious, which are confirmed by the cellular structures obtained from smoked foil. The ZND induction zone length (Δ_I) analysis confirms Δ_I is shorter at higher initial pressure, under this condition detonation is more sensitive and easier to survive from failure as it enters into the spiral section.     

The propagation mechanism of detonation wave in a round tube filled with larger blockage ratio orifice plates

In this study, the detonation propagation mechanisms for the stoichiometric hydrogen-oxygen mixture are explored systematically in a circular tube with 6-m in length and an inner diameter of 90-mm. The continuous orifice plates with BR = 0.93 are adopted to investigate the characteristics of detonation diffraction, failure and initiation. High-speed piezoelectric pressure transducers are used to obtain the average velocity, and the smoked foil technique is adopted to record the detonation cellular patterns. The results indicate that three various propagation regimes can be observed, i.e., steady detonation, quasi-detonation and fast flame. In the smooth tube, only the steady detonation and fast flame modes are seen. When the initial pressure is greater than the critical value, the detonation can propagate at about the theoretical CJ velocity. Near the critical pressure, a sudden velocity drop is observed. Of note is that the single-headed spin and double-headed detonation cannot occur because of the limitation of the aspect ratio. In the tube filled with obstacles, the averaged wave velocity is decayed severely. Only the mechanisms of the quasi-detonation and fast flame can be seen. In the quasi-detonation mode, the critical value of d/λ is greater than 7.36, which is far larger than 1. Two different detonation ignition regimes produced by the shock reflection from the wall are observed, i.e., the initiation positions occur in the vicinity of the tube wall and the surface of the orifice plate.     

The evolution and cellular structure of a detonation subsequent to a head-on interaction with a shock wave

This paper analyzes the results of a head-on collision between a detonation and a planar shock wave. The evolution of the detonation cellular structure subsequent to the frontal collision was examined through smoked foil experiments. It is shown that a large reduction in cell size is observed following the frontal collision, and that the detonation cell widths are correlated well with the chemical kinetic calculations from the ZND model. From chemical kinetic calculations, the density increase caused by shock compression appears to be the main factor leading to the significant reduction in cell size. It was found that depending on the initial conditions, the transition to the final cellular pattern can be either smooth or spotty. This phenomenon appears to be equivalent to Oppenheim's strong and mild reflected shock ignition experiments. The difference between these two transitions is, however, more related to the stability of the incident detonation and the strength of the perturbation generated by the incident shock.     

Numerical study on the characteristics of rotating detonation wave with multicomponent mixtures

In order to investigate the effects of gas mixture components on the combustion characteristics of rotating detonation wave, two-dimensional simulation is presented to simulate the propagation process of rotating detonation wave with different methane conversions. The results indicate that there are five propagation modes of rotating detonation wave with different components: single-wave mode, single wave with counter-rotating components mode, double-waves mode, triple-waves mode and quadruple-waves mode. The detonation wave propagates along the forward direction in all five modes. With the increase of methane conversion, multi-wave mode appears in the combustion chamber. The fuel component has a great influence on the heat release ratio of detonation combustion. The velocity of detonation wave decreases with the increase of methane conversion. With the increase of methane conversion, the chemical reaction rate gradually increases, which leads to the intensification of chemical reaction on the deflagration surface. The reaction on the deflagration surface develops to the unburned fuel zone, which eventually leads to the formation of compression waves and shock waves in the fuel refill zone. When the shock wave sweeps through the fresh premixed gas, the reactant is compressed to form a detonation point and then ignite the fuel. A new detonation wave is finally formed. The total pressure ratio decreases with the increasing methane conversion, and the uniformity of the total pressure of outlet decreases with increasing methane conversion.     

Modeling of attenuation and suppression of cellular detonation in the hydrogen-air mixture by circular obstacles

The results of numerical study of the interaction of the gaseous detonation with the regular obstacle consisting of checkered elements with circular cross section are presented. The aim of this work is to identify and generalize the parameters affected the attenuation of a cellular detonation propagating in a premixed stoichiometric hydrogen-air mixture. Studies of such problems are aimed at studying issues related to explosion and fire safety in the operation of highly efficient gaseous fuels, which are currently very widespread. As a result, the dependencies of the leading shock wave propagation velocity on the obstacle geometry are obtained. The contribution of each of the considered parameters to the detonation wave velocity deficit is estimated. Maps of detonation suppression and re-initiation modes for varying barrier parameters are obtained.     

Effects of confinement on detonation in H2–O2 mixture with transverse concentration gradient

Since hydrogen has wide flammability limit and low ignition energy, it could be easily ignited and be easy for the transition to a detonation, leading to extremely serious impacts in explosion accidents or extremely high combustion effeciency in the propulsion. In the field of explosion accidents and the combustion chamber of propulsion systems, hydrogen mixtures are more likely to be highly non-uniform and a detonation usually propagates in a non-homogeneous medium. The work studies behaviors of detonations in non-homogenous medium by a high-resolution simulations. We widen computational domain and steepen the gradient to weaken the role of transverse wave on cellular detonations propagating in the medium with transverse concentration gradient and to reveal the interaction of longitudinal shock with reaction wave. The results show that characteristics of detonations in nonuniform medium is controlled by coupling role of gradient and confinement. As a domain is sufficient wide, the reflection wave is rather weak so that the detonation takes on galloping propagation, with a single-head mode. As the width is mediate, detonation cell takes on highly irregularity, similar to that of highly unstable detonation. However, in the narrow domain, steepening gradient plays a key role while confinement becomes minor in detonation propagation.     

Oblique detonation wave stability around a spherical projectile by a high time resolution optical observation

Spherical projectiles were launched into detonable mixtures over a wide range of projectile velocities from near to about 1.8 times the Chapman–Jouguet (C–J) velocity. Oblique detonation waves (ODWs) and shock-induced combustions (SICs) stabilized around the projectiles were visualized with high time and high spatial resolutions using the Schlieren technique and a high-speed camera with a 1-μs frame speed. Unsteady wave structures called Straw Hat type structures consisting of a SIC region followed by a C–J ODW were observed near stabilizing criticalities of a C–J ODW, and they were divided into two propagation types, depending on whether the C–J ODW could be stabilized [11], [12], [14]. In the present study, we suggested wave structures of the Straw Hat types based on our examination of dozens of continuous images. Triple points were observed at the intersection of a bow shock, a C–J ODW and a transverse detonation or shock wave when projectile velocities were slightly higher than C–J velocities. Onsets of local explosions in the SIC region for stabilizing the ODW in the Straw Hat type structures have been reported [14]. We observed this stabilizing mechanism by visualizing onsets of periodical local explosions and their transition to spherical detonation waves when the projectile velocity was much higher than the C–J velocity. We also determined stabilizing criticalities using a stoichiometric acetylene-oxygen mixture diluted with argon or krypton in 50% or 75% volumetric fractions, respectively. We found that the stabilizing criticalities did not depend only on the ratio of the projectile diameter and the cell size of the mixture.