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.     

Energy release effect of mixture on single spinning detonation structure

Unsteady three-dimensional numerical simulation on a single spinning detonation in a circular tube are presented in order to understand the effects of energy release of the mixture on the detonation structure. Overall structures of the spinning detonations such as the shock structure around the spin head, the long pressure trail, and the track angle on the wall are not affected by these effects because they depend on the specific heat ratio of the products which has approximately a constant value. The calculated averaged detonation velocities on the symmetry axis during one cycle decrease inversely with an exponential curve to become the value lower than the CJ detonation velocity. Those for p₀ = 0.1 MPa and p₀ = 0.01 MPa become approximately 0.98 D_CJ and 0.92 D_CJ, respectively, because the energy release in the CJ state for p₀ = 0.01 MPa is 10% lower than that for p₀ = 0.1 MPa. The state of gas behind the head of spinning detonation is also evaluated by the classical oblique shock theory and equilibrium calculation by using the track angle, shock wave angle, and detonation velocity in order to compare with the present and other researcher’s numerical results. The effects of the energy release in the mixture are large on the strength of the transverse detonation.     

Three-dimensional detonation structure and its response to confinement

Three-dimensional (3D) detonation simulations solving the compressible Navier-Stokes equations with detailed chemistry are performed in both square channel and round tube geometries. The simulations are compared with each other and with two-dimensional (2D) channel simulations and round tube experiments of identical mixture and conditions (stoichiometric hydrogen-oxygen with 3000 PPMv ozone at 300 K and 15 kPa) with the goal of understanding the effect of confinement and boundaries on detonation structure. Results show that 3D detonations propagate with highly inhomogeneous blast dynamics, where blasts emerge not only from intersections of two transverse waves (similar to 2D propagation) but also from intersections of many transverse waves (unique to 3D detonations in the confinements tested). Intersections of many transverse waves lead to extreme thermodynamic states and highly overdriven wave velocities, well in excess of those seen in the ZND model and in 2D simulations. 3D simulations in the square tube show highly regular blast latticing, smaller detonation cells, and highly oscillatory velocities when compared to the round tube simulations. Round tube simulations show more spatially non-uniform blast dynamics. The conclusions reached in the current work are found irrespective of numerical grid resolution.     

Sensitizing gaseous detonations for hydrogen/ethylene-air mixtures using ozone and H2O2 as dopants for application in rotating detonation engines

The effect of ozone and hydrogen peroxide as dopants on hydrogen-air and ethylene-air detonations was investigated with one-dimensional ZND calculations. Also, the effects of dopants were studied numerically with argon and helium as diluents with an aim to reduce the temperature of detonation products while maintaining a detonation wave of sufficient strength such that its propagation is stable near its propagation limits. The primary goal of the present investigation is to isolate the chemical kinetic effects from fluid and gas dynamic effects by altering the ignition chemistry of an unburned mixture without significantly changing its thermodynamic and physical properties. The ZND calculations demonstrate that the addition of O₃ and H₂O₂ in small quantities will substantially reduce the induction length (Δ_i) and time (τ_i), even with higher diluent percentages of argon and helium, making it a viable solution for reducing the operating temperatures of rotating detonation engines (RDEs). The effects of O₃ and H₂O₂ are also studied numerically at lower equivalence ratios for H₂/C₂H₄-air detonations with an aim to reduce the post-detonation temperatures below 2000 K for its application in practical engine cycles. Also, the efficacy of CF₃I, as an ignition promoter at small quantities, is studied numerically for hydrogen-air detonations, and its performance is compared with O₃ and H₂O₂.     

Numerical simulations of hydrogen detonations with detailed chemical kinetics

Time-dependent, multidimensional simulations of unstable propagating detonations were performed using a detailed thermochemical reaction model for a stoichiometric argon-diluted hydrogen–oxygen mixture at low pressures and a hydrogen–air mixture at atmospheric pressure. Detonation cells computed for the low-pressure, dilute H₂–O₂–Ar systems were regular in shape, and their sizes compared reasonably well with experimental observations. The computed H₂–air cells at atmospheric conditions were qualitatively different from those observed in experiments, and their widths range from less than 1 mm to nearly 5 mm with multilevel hierarchal structures. The effective activation energy of the H₂–air mixture, based on constant-volume ignition delay times computed using the detailed thermochemical model, varies between 5 and 40 over the range of post-shock temperatures and pressures in the simulations and is, on average, significantly larger than expected based on the regularity of experimental cellular patterns. Analysis of the simulations suggests that vibrational relaxation of the gas molecules, a process which is ignored when calibrating detailed chemical reaction models, occurs on time scales similar to the ignition delay times for the detonations and may be a source of discrepancy between numerical and experimental results.     

Pressure loading of detonation waves through 90-degree bend in high pressure H2–O2–N2 mixtures

Detonation experiments are conducted to investigate the detonation wave behavior in steam pipelines of boiling water reactors. Accumulated gases in BWRs are stoichiometric hydrogen/oxygen mixtures diluted with steam at 7 MPa. In the experiment, flammable gas mixture diluted with nitrogen at room temperature and up to 5 MPa is used to achieve equivalent detonation condition. Two test pieces are used, one is straight tube and the other is 90-degree bend. No initial pressure dependency in detonation wave behavior is observed in the experiments. However, in the straight tube tests, detonation velocities higher than theoretical values are measured when the initial pressures are greater than 2.3 MPa. This result is considered as attribution of real gas effect. In the 90-degree bend experiments, pressure time histories reveal pressure loads greater than the straight tube portion at two locations. One is a high pressure peak at the extrados of the bend and the other is a double pressure peak just downstream of the bend outlet. Second pressure peak just downstream of the bend outlet is due to transverse wave propagation. Additionally, the largest impulse is observed not at the extrados of the bend but at the intrados of bend outlet. These results show the importance of more investigations on transverse wave behaviors in failure potential evaluation.     

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.     

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.     

Accelerative expansion and DDT of stoichiometric ethylene/oxygen flame rings in micro-gaps

Acceleration and transition to detonation of expanding flame rings ignited at the center of 260 μm and 120 μm gaps between parallel flat pates were experimentally studied. The micro-spacing was initially filled with stoichiometric ethylene/oxygen mixtures at ambient pressure and temperature. Visualizations showed that the outward propagating reaction wave was initially smooth and circular, but petal-like wrinkles quickly developed on the flame ring. Flame wrinkles appeared earlier and closer to the ignition point as the gap width became smaller. The flame underwent fast acceleration during the onset of flame wrinkling, but the acceleration was relatively mild as the wrinkled flame ring continued to expand. Time exponents for the accelerative growth of corrugated flame rings were identical in the two highly confined gaps. The flame ring underwent deflagration-to-detonation transition as the propagation velocities abruptly surged from 1000 m/s to over 2000 m/s. The arc-shaped detonation waves initiated from local explosion spots on the flame ring were propagating at near Chapman–Jouguet velocities. The induction distance and time for detonation transition were both shorter in the smaller gap. Detonation cell patterns and the initiation locations were also clearly recorded through soot film visualizations.     

爆轰模型熵问题的探讨

 爆轰模型过程终点熵最低的问题长时间困扰着爆轰科学。牛顿力学对于时间t→-t反演不变,忽略热力学而只用力学方法研究不可逆爆轰过程可能产生不合理的结果。CJ和ZND模型中的有序假设,即爆轰产物粒子朝着同一方向作有序运动的假设,决定了终点熵最低和不处于热力学平衡态。把CJ和ZND模型的某些结论绝对化,阻碍建立熵最高的爆轰模型。     

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.     

Strong flame acceleration and detonation limit of hydrogen-oxygen mixture at cryogenic temperature

A series of experiments were carried out in a closed tube at cryogenic temperature (77 K) for hydrogen-oxygen mixtures. Flame propagation speed and overpressure were measured by optical fibers and pressure sensors, respectively. The first and second shock waves were captured in the cryogenic experiments, although the shock waves always precede the flames in all cases indicating the absence of stable detonation. However, strong flame acceleration was observed for all situations, which is consistent with the prediction by expansion ratio and Zeldovich number. Besides, the tube diameter and length are also critical for flame acceleration to supersonic. All the flames in this work accelerate drastically reaching the C-J deflagration state. But at 0.4 atm, only fast flame is formed, while at higher initial pressures, the flame further accelerates to a galloping mode manifesting a near-limit detonation, which could be indicated by the stability parameter $\chi$.     

Two-dimensional numerical simulation on galloping detonation in a narrow channel

The numerical simulations of the two-dimensional galloping detonation performed by using two-dimensional full Navier–Stokes simulations with a detailed chemistry model are presented. The detonation in a narrow channel with d = 5 mm, which is approximately twice the half-reaction length of hydrogen, shows a feature of galloping detonation with two initiations during its propagation under the laminar flow assumption. The distance between these two initiations is approximately 1300 mm, which causes the induction time behind the leading shock wave. As the channel width increases, the galloping feature diminishes. The detonation propagates approximately 4% lower than D_CJ for d = 10 and 15 mm. By increasing the channel width, the strength of the detonation increases, as shown in the maximum pressure histories. The effects of turbulence behind the detonation show that the galloping feature disappears, although its propagation velocity becomes 0.9 D_CJ. The strength of the detonation becomes significantly weak compared with the detonation propagating in the wide channel widths, and this feature is similar to the laminar assumption. The trend of the velocity deficits in the NS simulations agrees fairly well with the trend of the modified ZND calculations with η = 0.25.     

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 study on spinning detonations

Spinning detonations in both a circular tube and a square tube are presented in order to reveal characteristics of spinning modes by using three-dimensional simulations with a detailed chemical reaction model. The present results show a feature of a single spinning detonation which was discovered in 1926. The shock patterns in both cases are similar except the pressure trail, however, the shock wave angles and the shock wave lengths are shown to be dependent on the cross section configuration of the tube. The pitch angle, the track angle, the Mach stem angle, and the incident shock angle on the tube wall in the numerical results agree well with those in the experimental ones, and they are independent of the compositions of mixture, tube diameters, and initial pressures.     

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.     

A flame technique to isolate the detonation/product interface relevant to rotating detonation engines

A novel experimental technique is proposed to study the detonation propagation in a layer of non-reacted gas weakly confined by combustion products. This problem is relevant to rotating detonation engines, where transverse detonations are confined by products of a previous rotation cycle, and other applications such as industrial safety. The experimental technique utilizes a flame ignited along the top wall in a long channel. The preferential growth of the flame along the long direction of the channel creates a finger flame and permits to create a narrow layer of unburned gas. A detonation ignited outside of this layer then propagates through the layer. This permits to conduct accurate observations of the detonation interaction with the inert gas and determine the boundary condition of the interaction. The present paper provides a proof-of-concept demonstration of the technique in a 3.4 m by 0.2 m channel, in which long finger flames were observed in ethylene-oxygen mixtures. The flame is visualized by high-speed direct luminosity over its entire travel, coupled with pressure measurements. A direct simulation of the flame growth served to supplement the experiments and evaluate the role of the induced flow by the flame growth, which gives rise to a non-uniform velocity distribution along the channel length. Detonation experiments were also performed at various layer heights in order to establish the details of the interaction. The structure was visualized using high speed Schlieren video. It was found that an inert shock always runs ahead of the detonation wave, which gives rise to a unique double shock reflection interaction.     

Weak detonations,their paths and transition to strong detonation

Previously, a quasi-steady form of the classical Rankine–Hugoniot weak detonation has been shown to play an integral part in describing certain forms of detonation initiation, arising during an intermediate stage between the thermal ignition of the material and the first appearance of a strong detonation with Zeldovich–von Neumann–Döring (ZND) structure. In this paper, we use a parametric variable integration to calculate numerically the path of the weak detonation in two important initiation scenarios, shock-induced and initial disturbance-induced transition to detonation, via a large activation energy induction domain model. The influence that the nature of the path may have on the weak detonation structure is also discussed. In each case these calculations enable us to predict how, where and when the transition to a strong detonation with ZND structure will occur. Explanations for several phenomena observed in both experiments and numerical studies on transition to detonation are also uncovered by these calculations.     

The re-initiation of cellular detonations downstream of an inert layer

The current work aims to examine how the nature of cellular instabilities controls the re-initiation capability and dynamics of a gaseous detonation transmitting across a layer of inert (or non-detonable) gases. This canonical problem is tackled via computational analysis based on the two-dimensional, reactive Euler equations. Two different chemical kinetic models were used, a simplified two-step induction-reaction model and a detailed model for hydrogen-air. For the two-step model, cases with relatively high and low activation energies, representing highly and weakly unstable cellular detonations, respectively, are considered. For the weakly unstable case, two distinct types of re-initiation mechanisms were observed. (1) For thin inert layers, at the exit of the layer the detonation wave front has not fully decayed and thus the transverse waves are still relatively strong. Detonation re-initiation in the reactive gas downstream of the inert layer occurs at the gas compressed by the collision of the transverse waves, and thus is referred to as a cellular-instability-controlled re-initiation. (2) If an inert layer is sufficiently thick, the detonation wave front has fully decayed to a planar shock when it exits the inert layer, and re-initiation still occurs downstream as a result of planar shock compression only, which is thus referred to as a planar-shock-induced re-initiation. Between these two regimes there is a transition region where the wave front is not yet fully planar, and thus perturbations by the transverse waves still play a role in the re-initiation. For the highly unstable case, re-initiation only occurs via the cellular-instability-controlled mechanisms below a critical thickness of the inert layer. Additional simulations considering detailed chemical kinetics demonstrate that the critical re-initiation behaviors of an unstable stoichiometric mixture of hydrogen-air at 1 atm and 295 K are consistent with the finding from the two-step kinetic model for a highly unstable reactive mixture.     

Near limit behavior of the detonation velocity

The behavior of the detonation velocity near the limits is investigated. Circular tubes of diameters 65, 44 and 13 mm are used. To simulate a quasi two-dimensional rectangular geometry thin annular channels are also used. The annular channels are formed by a 1.5 m long insert of a smaller diameter tube into the larger outer diameter detonation tube. Premixed mixtures of C₂H₂ + 2.5O₂ + 70%Ar, CH₄ + 2O₂ and C₂H₂ + 5N₂O + 50%Ar are used in the present study. The high argon dilution stoichiometric C₂H₂ + 2.5O₂ mixture has a regular cell size and piecewise laminar reaction zone and thus referred to as “stable”. The other two mixtures give highly irregular cell pattern and a turbulent reaction zone and are hence, referred to as “unstable” mixtures. Pressure transducers and optical fibers spaced 10 cm apart along the tube are used for pressure and velocity measurements. Cell size of the three mixtures studied is also determined using smoked foils in both the circular tubes and annular channels. The ratio d/λ (representing the number of cells across the tube diameter) is found to be an appropriate sensitivity parameter to characterize the mixture. The present results indicate that well within the limit, the detonation velocity is generally a few percent below the theoretical Chapman–Jouguet (CJ) value. As the limit is approached, the velocity decreases rapidly to a minimum value before the detonation fails. The narrow range of values of d/λ of the mixture where the velocity drops rapidly is found to correspond to the range of values for the onset of single headed spinning detonations. Thus we may conclude that the onset of single headed spin can be used as a criterion for defining the limits. Spinning detonations are also observed near the limits in annular channels.