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.     

Numerical application of additive Runge-Kutta methods on detonation interaction with pipe bends

A detailed reaction model comprised of 9 species and 48 reactions is employed in simulating two-dimensional cellular detonations propagating through smooth pipe bends in a stoichiometric H₂/O₂ mixture diluted by Argon. Additive Runge-Kutta (ARK) methods are applied to solve the stiff reactive Euler equations, in which the stiff and non-stiff terms are solved implicitly and explicitly. The numerical results indicate that, as the regular cellular detonation wave propagating through the bend section, the diffraction near the inner wall causes an increase in detonation cell size while the detonation reflection occurring on the bottom wall leads to a decrease in cell size. In addition, an expansion wave is generated continuously. The expansion wave causes the failure as well as the partial failure of the detonations near the inner and outer walls, respectively. On the contrary, the transverse re-initiation waves evolve into a detonation in the decoupling zone just downstream of the bend outlet owing to continuous compression imposed by other transverse waves propagating right behind. Meanwhile, there exists a transition length after the detonation propagating out of the bend and entering the sloped tube section.     

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.     

Pulsating one-dimensional detonation in ammonia-hydrogen–air mixtures

In this study, one-dimensional detonations in ammonia/hydrogen-air mixtures are numerically investigated by solving the fully compressible Navier-Stokes equations with detailed chemistry. Pulsating instabilities with single-mode are observed during the detonation wave propagation, accompanied by periodic coupling and decoupling of the lead shock wave and the reactive front. The ratio between driver pressure and initial pressure determines the overdrive degree and thus the oscillatory mode of detonation for a premixture with certain composition. The effects of hydrogen dilution and mixture equivalence ratio on pulsating detonations are also examined under a constant driver pressure. The growing hydrogen fraction in fuel blends significantly increases the oscillation frequency. In addition, the pulsating detonation frequency rises with increasing equivalence ratio under fuel-lean conditions, peaks under stoichiometric conditions, and falls under fuel-rich conditions as the equivalence ratio increases further. Evolutions of reactants, main intermediate radicals, and products are analysed in both fuel-lean and fuel-rich conditions. A chemical explosive mode analysis further confirms the highly-autoignitive nature of the mixture in the induction zone between reaction front and shock front where thermal diffusion plays a negligible role.     

Detonability of natural gas–air mixtures

Direct initiation experiments were carried out in a 105 cm diameter tube to study detonation properties and evaluate the detonability limits for mixtures of natural gas (NG) with air. The natural gas was primarily methane with 1.5–1.7% of ethane. A stoichiometric methane–oxygen mixture contained in a large plastic bag was used as a detonation initiator. Self-supporting detonations with velocities and pressures close to theoretical CJ values were observed in NG–air mixtures containing from 5.3% to 15.6% of NG at atmospheric pressure. These detonability limits are wider than previously measured in smaller channels, and close to the flammability limits. Detonation cell patterns recorded near the limits vary from large cells of the size of the tube to spiral traces of spin detonations. Away from the limits, detonation cell sizes decrease to about 20 cm for 10% NG, and are consistent with existing data for methane–air mixtures obtained in smaller channels. Observed cell patterns are very irregular, and contain secondary cell structures inside primary cells and fine structures inside spin traces.     

Self-organized generation of transverse waves in diverging cylindrical detonations

Self-organized generation of transverse waves associated with the transverse wave instabilities at a diverging cylindrical detonation front was numerically studied by solving two-dimensional Euler equations implemented with an improved two-step chemical kinetic model. After solution validation, four mechanisms of the transverse wave generation were identified from numerical simulations, and referred to as the concave front focusing, the kinked front evolution, the wrinkled front evolution and the transverse wave merging, respectively. The propagation of the cylindrical detonation is maintained by the growth of the transverse waves that match the rate of increase in surface area of the detonation front to asymptotically approach a constant average number of transverse waves per unit length along the circumference of the detonation front. This cell bifurcation phenomenon of cellular detonations is discussed in detail to gain better understanding on detonation physics.     

Transverse waves resulting from pulsating instability of two-dimensional flames

We present results of fully compressible Navier–Stokes simulations of pulsating flame instabilities in two dimensions using single-step, first-order Arrhenius kinetics. Model parameters correspond to Zel’dovich and Lewis numbers of Ze = 9.5 and Le = 10, respectively, and flame Mach numbers M_L between 4.62 × 10⁻³ and 2.31 × 10⁻². The results show that the pulsating instability creates two types of transverse waves: deflagrations and detonations. Both types of waves can coexist for the same reactive system, but transverse detonations become more likely as M_L increases. The transverse detonations observed for our model system are of the intermediate type with most of the chemical energy release accompanying the pressure rise. They propagate inside the large preheat zone of the pulsating flame and do not spread into cold material. The results expand our knowledge of possible new phenomena associated with pulsating instability.     

Velocity fluctuation near the detonation limits

In this study, the velocity fluctuation near the detonation limits is investigated experimentally. Five explosive mixtures in five different diameter tubes were used and the choice of the mixtures included those considered as “stable” with regular cellular pattern and “unstable” with highly irregular cellular pattern. Photodiodes spaced at regular intervals along the tube were used to measure the detonation velocity. Piezoelectric transducers were also used to record the pressure profiles. Smoked foils were used to register the cellular detonation structure. Away from the limits, the detonation is found to propagate at a steady velocity throughout the length of the tube and the fluctuations of the local velocity are generally small. For stable mixtures with high argon dilution, the onset of the detonation limits is indicated by an abrupt drop in the detonation velocity to about 0.4V_CJ after a short distance of travel. The detonation may continue to propagate at this low velocity before decaying eventually to a deflagration wave. For deflagrations the optical detector sometimes failed to register a signal due to low luminosity of the front. In unstable mixtures, galloping detonations are observed only in small diameter tubes (e.g., D = 12.7, 3.2 and 1.5 mm). A large number of fairly reproducible cycles of galloping detonations can be observed in very small diameter tubes. In large diameter tubes (e.g., D = 31.7 and 50.8 mm), no galloping detonations are observed in all stable and unstable mixtures. For stable mixtures, no galloping detonations are observed even in small diameter tubes of D = 3.2 and 1.5 mm. Smoked foils records show that the cellular detonation structure changes from multi-headed to single-headed spin as the limit is approached. In a galloping detonation cycle, a decay from multi-headed to single-headed detonation is observed. However, the cellular structure vanishes for further decay of the galloping detonation to the low velocity phase of the galloping cycle. Although galloping detonations could be considered to define the boundary for detonation limits, this definition lacks generality since galloping detonations are not always observed in all mixtures and in all tube diameters. Thus the onset of single-headed spin is perhaps the most appropriate criterion of the detonation limits in tubes.     

Experimental and numerical studies on detonation failure and re-initiation behind a half-cylinder

Mach reflection causes the re-initiation of decoupled detonation owing to changes in the boundary. A complementary series of experiments and numerical simulations, illustrating detonation failure and subsequent reinitiation processes, have been presented. Immediately across the half-cylinder, the decoupled detonation owing to the diffraction effect wave is reflected on the bottom wall to form a regular reflection, and then changes into the Mach reflection, which further determines the detonation reinitiation. Two different reinitiation modes after detonation wave diffraction were observed for the stable mixtures: the direct Mach reflection re-initiation mode and Mach reflection combined with the transverse detonation. However, for unstable detonations, a different reinitiation mode was obtained, whereby the development of intrinsic instabilities resonates with the reflection on the bottom wall, rendering the Mach reflection randomly occurring or even absent. The critical limit of detonation failure is characterized by the radius of the half-cylinder and the cell size. In addition, the transition length from regular to Mach reflection was measured to reveal the length-scale effect on the process.     

Initiation of spherical detonation in hydrogenair

Spherical detonation has been initiated in a range of mixtures of hydrogen and air, at one atmosphere initial pressure, by Tetryl charges of mass (0.78–2.40) × 10^?3 kg. The results are in accordance with an earlier experiment by Cassut but contrary to a recent prediction of Lee. A theoretical model embracing the full kinetic scheme for hydrogen oxidation fits the experimental detonability data and predicts the variation of detonability with concentration over a much wider range. An important conclusion from the model study is that it predicts for the first time for spherical detonation the existence of concentration limits to detonability. A kinetic explanation is offered for these limits which are approximately 13–70% v hydrogen in air.     

Characteristic of rotating detonation wave in the H2/Air hollow chamber with Laval nozzle

To pinpoint the relationship between high frequency tangential instability(HFTI) and continuous rotating detonation (CRD), series of H₂/Air rotating detonations are experimentally achieved in the hollow chamber with Laval nozzle. The contraction ratio of the nozzle has a significant effect on the detonation. The detonation waves number increases with the increasing of equivalence ratio (ER) or nozzle contraction ratio. Based on its character, a new type of detonation is defined as two dominant peak one wave mode (TDPO). The velocities of detonation waves propagating in this new mode are larger than the Chapman-Jouguet (CJ) theoretic value. On the assumption that the reflection wave is rotated with the detonation wave, this mode is well illustrated. The forming process of two waves is also given. The results show that the appearance of combustion mode is relative to the reflection wave generated at the contraction section of the nozzle. The inner mechanism of the refection wave is illustrated. These works make a foundation to investigate the relationship between rotating detonation and tangential instability.     

Experimental study on transmission of an overdriven detonation wave from propane/oxygen to propane/air

Two sets of experiments were performed to achieve a strong overdriven state in a weaker mixture by propagating an overdriven detonation wave via a deflagration-to-detonation transition (DDT) process. First, preliminary experiments with a propane/oxygen mixture were used to evaluate the attenuation of the overdriven detonation wave in the DDT process. Next, experiments were performed wherein a propane/oxygen mixture was separated from a propane/air mixture by a thin diaphragm to observe the transmission of an overdriven detonation wave. Based on the characteristic relations, a simple wave intersection model was used to calculate the state of the transmitted detonation wave. The results showed that a rarefaction effect must be included to ensure that there is no overestimate of the post-transmission wave properties when the incident detonation wave is overdriven. The strength of the incident overdriven detonation wave plays an important role in the wave transmission process. The experimental results showed that a transmitted overdriven detonation wave occurs instantaneously with a strong incident overdriven detonation wave. The near-CJ state of the incident wave leads to a transmitted shock wave, and then the transition to the overdriven detonation wave occurs downstream. The attenuation process for the overdriven detonation wave decaying to a near-CJ state occurs in all tests. After the attenuation process, an unstable detonation wave was observed in most tests. This may be attributed to the increase in the cell width in the attenuation process that exceeds the detonability cell width limit.     

Effect of orifice plate on the transmission mechanism of a detonation wave in hydrogen-oxygen mixtures

In this paper, a square orifice plate with 60 mm thick and the blockage ratio (BR) of 0.889 is employed to systematically explore the transmission regime of a steady detonation wave in hydrogen-oxygen mixtures. The influence of hydrogen mole fraction is also considered. The average velocity of combustion wave can be determined by evenly mounting eight high-speed pressure sensors on the tube wall, and the detonation cellular patterns can be also registered by the soot foil technique. The experimental results indicate that for the condition of smooth tube, the hydrogen concentration limits range of detonation successful propagation is 37.5%–73.68%. Two propagation modes can be obtained, i.e., the regimes of fast flame and steady detonation. The hydrogen concentration limits range is narrowed to 42.53%–69.51% in the tube with a square orifice plate. Three propagation regimes are observed: (1) near the low limit, a steady detonation wave can be produced before the obstacle, and the phenomenon of detonation decay is seen across the square orifice plate because of the influence of diffraction resulting in the mechanism of detonation failure. The failed detonation wave is not re-ignited because of the lower hydrogen concentration; (2) as the hydrogen mole fraction is increased to 42.53%, the mechanism of detonation re-ignition can be seen after the detonation decay. Well within the limits, the same detonation re-initiation phenomenon also can be observed; (3) as the hydrogen concentration is further enhanced to 69.7% beyond the upper limit, a stable detonation wave is not produced prior to the orifice plate, and the combustion wave front maintain the mode of fast flame until the end of the channel. Finally, it can be found that the detonation wave can successfully survive from the diffraction only when the effective diameter (d_eff) is at least greater than one cell size (λ).     

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.     

Numerical simulation of the influence of confined multi-point ignited H2–O2 mixture on the propagation of shock waves towards a deformable plate

The study of shock wave propagation in a detonation chamber is of great importance as a part of the plate forming process. Investigations related to the effects of premixed gas detonation on the deflection of a plate require in-depth examination. An Eulerian-Lagrangian numerical simulation is conducted using the space-time conservation element and solution element method of LS-DYNA software to study the effect of confined multi-point ignited gaseous mixture on the dynamic response of thin plates clamped at the end of a combustion chamber. The FSI couples a Lagrangian finite element solver with a Eulerian fluid solver in a 2D space with detailed chemistry of H₂–O₂ mixture. The solution contains the detonation wave propagation through the combustion chamber and its interaction with the plate. The influence of variation in the multi-point ignition locations and combustion chamber dimensions on the pressure history and plate deflection is studied. To verify the model, a comparison with the experimental study is carried out using an adjustable model representative of the real experiment. The verified model is used to link the evolution of plate shape with the arrival time and intensity of shock waves within the chamber. It is found that a longer distance between the ignition point and the plate intensifies the ultimate deflection of the plate. In addition, a fairly large combustion area employed in a direction rather than transverse to the plate surface is unable to influence the ultimate deformation of the plate.     

High speed turbulent deflagrations and transition to detonation in H2air mixtures

An experimental investigation on flame acceleration and transition to detonation in H₂air mixtures has been carried out in a tube which had a 5 cm cross-sectional diameter and was 11 m long. Obstacles in the form of a spiral coil (6 mm diameter tubing, pitch 5 cm, blockage ratio BR = 0.44) and repeated orifice plates spaced 5 cm apart with blockage ratios of BR = 0.44 and 0.6 were used. The obstacle section was 3 m long. The compositional range of H₂ in air extended from 10 to 45%, the initial pressure of the experiment was 1 atm, and the mixture was at room temperature. The results indicate that steady-state flame (or detonation) speeds are attained over a flame travel of 10–40 tube diameters. For H₂ ? 13% maximum flame speeds are subsonic, typically below 200 m/s. A sharp transition occurs at about 13% H₂ when the flame speed reaches supersonic values. A second transition to the so-called quasi-detonation regime occurs near the stoichiometric composition when the flame speed reaches a critical value of the order of 800 m/s. The maximum value of the averaged pressure is found to be between the normal C-J detonation pressure and the constant volume explosion value. Of particular interest is the observation that at a critical composition of about 17% H₂ transition to normal C-J detonation occurs when the flame exits into the smooth obstacle-free portion of the tube. For compositions below 17% H₂, the high speed turbulent deflagration is observed to decay in this portion of the tube. The detonation cell size for 17% H₂ is about 150 mm and corresponds closely to the value of πD that has been proposed to designate the onset of single-head spinning detonation, in this case for the 5 cm diameter tube used. This supports the limit criterion, namely, that for confined detonations in tubes, the onset of single-head spin gives the limiting composition for stable propagation of a detonation wave.     

Supersonic driven detonation dynamics for rotating detonation engines

In this paper we present the first exploration of detonation wave propagation dynamics in premixed supersonic flows using a novel rotating detonation engine (RDE) configuration. An RDE with a coupled linear extension, referred to as ρDE, is used to divide detonations traveling radially in the RDE into linearly propagating waves. A tangential propagating wave is directed down a modular tangential linearized extension to the engine for ease of optical diagnostics and hardware configuration investigations. A premixed Mach 2 supersonic linear extension is coupled to the ρDE to investigate the effects of varying crossflow configurations for detonation propagation, particularly the interaction between detonations and supersonic reactive mixtures. Detonation waves are generated at the steady operating frequency of the RDE and visualized using high speed schlieren and broadband OH* chemiluminescence imaging. The stagnation pressure was varied from over- to ideally-expanded supersonic regimes. Experimental analysis of detonation interaction with the supersonic regimes show that the detonation propagates freely in the ideally-expanded regime. Deflagration-to-detonation transition (DDT) occurs in the over-expanded regime. Based on the data collected, the DDT process favors supersonic flow with higher source pressures.     

Critical energy for direct initiation of spherical detonations in H2/N2O/Ar mixtures

Although the detonation phenomenon in hydrogen-nitrous oxide mixtures is a significant issue for nuclear waste storage facilities and development of propulsion materials, very limited amount of critical energy data for direct initiation - which provides a direct measure of detonability or sensitivity of an explosive mixture − is available in literature. In this study, the critical energies for direct blast initiation of spherical detonations in hydrogen-nitrous oxide-Ar mixtures obtained from laboratory experiments and theoretical predictions at different initial conditions (i.e., different initial pressure, equivalence ratio and amount of argon dilution) are reported. In the experiments, direct initiation is achieved via a spark discharge from a high voltage and low inductance capacitor and the initiation energy is estimated accordingly from the current output. Characteristic detonation cell sizes of hydrogen-nitrous oxide-Ar mixtures are estimated from chemical kinetics using a recently updated reaction mechanism. A correlation expression is developed as a function of initial pressure, argon dilution and equivalence ratio, which is fitted to provide good estimation of the experimental measured data. The direct link between cell size and critical energy for direct blast initiation is then analyzed. Good agreement is found between experimental results and theoretical predictions, which make use of the cell size estimation correlation and the semi-empirical surface energy model. The effects of the initial pressure, equivalence ratio and the amount of Ar dilution on the critical initiation energy H₂-N₂O-Ar mixtures are investigated. By comparing the critical energies with those of H₂-O₂-Ar mixtures, it is shown that H₂-N₂O mixtures are more detonation sensitive with smaller initiation energies than H₂-O₂ mixtures at the same initial pressure, equivalence ratio and amount of argon dilution, except for higher diluted condition with amount of argon in the mixture above 20%. Attempt is made to explain the critical energy variation and comparison between the two H₂-N₂O-Ar and H₂-O₂-Ar mixtures from the induction length analysis and detonation instability consideration.     

Acceleration of laminar hydrogen/oxygen flames in a tube and the possible onset of detonation

The possibility is analysed of a laminar flame accelerating along a cylindrical tube, closed at one end, and inducing a deflagration to detonation transition in a stoichiometric H₂/O₂ mixture. The pressure and temperature ratios at the ensuing shock wave increase, as do laminar burning velocities, while autoignition delay times decrease. Combined with appreciable elongation of the flame, these enhance the strength of the shock. The conditions necessary for delay times of 0.05, 0.1, 1.0 and 5.0 ms, at an unburned mixture critical Reynolds number of 2300, are computed for different tube diameters. Probable consequences of the different delay times and hot spot reactivity gradients, including detonation, are all considered. The probability of a purely laminar propagation leading to a detonation is marginal. Only when the initial temperature is raised to 375 K, do purely laminar detonations become possible in tubes of between about 0.5 and 1.35 mm diameter.