Propagation of gaseous detonation across inert layers

In rotating detonation engines and explosion accidents, detonation may propagate in an inhomogeneous mixture with inert layers. This study focuses on detonation propagation in a stoichiometric H₂/O₂/N₂ mixture with multiple inert layers normal to the detonation propagation direction. One- and two-dimensional simulations considering detailed chemistry are conducted. The emphasis is placed on assessing the effects of inert layer on detonation reinitiation/failure, detonation propagation speed, detonation cell structure and cell size. Specifically, the inert layer thickness and the spacing between two consecutive inert layers are varied. Either detonation reinitiation or failure across the inert layers is observed. It is found that successful detonation reinitiation occurs only at relatively small values of the inert layer thickness and spacing. For each given value of the inert layer spacing, there is a critical inert layer thickness above which detonation fails after crossing the inert layers. This critical inert layer thickness is found to decrease as the inert layer spacing increases. The detailed process of detonation reinitiation across the inert layers is analyzed. The interaction between the transverse shock waves is shown to induce local autoignition/explosion and eventually over-driven detonation development in the reactive layer. The averaged detonation propagation speed in the inhomogeneous mixture is compared to the CJ speed and very good agreement is achieved. This indicates that the inert layer does not affect the detonation propagation speed once successful detonation reinitiation happens. Unlike the detonation speed, the detonation cell structure and cell size are greatly affected by the inert layer results. For the first time, large cellular structure with size linearly proportional to the inert layer spacing is observed for detonation propagation across inert layers. Besides, a double cellular structure is observed for relatively large spacing between inert layers. The formation of double cellular structure is interpreted.     

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.     

Three-dimensional numerical thrust performance analysis of hydrogen fuel mixture rotating detonation engine with aerospike nozzle

The propulsive performance for an H₂/O₂ and H₂/Air rotating detonation engine (RDE) with conic aerospike nozzle has been estimated using three-dimensional numerical simulation with detailed chemical reaction model. The present paper provides the evaluation of the specific impulse (I_sp), pressure gain and the thrust coefficient for different micro-nozzle stagnation pressures and for two configurations of conic aerospike nozzle, open and choked aerospike. The simulations show that regardless of the nozzle, increase the micro-nozzles stagnation pressure increases the mass flow rate, the pre-detonation gases pressure and consequently the post-detonation pressure. This gain of pressure in the combustion chamber leads to a higher pressure thrust through the nozzle, improving the I_sp. It was also found that the choked nozzle increases the chamber time-averaged static pressure by 50–60% compared with the open nozzle, inducing higher performance for the same reason explained before.     

氢气-空气混合物中瞬态爆轰过程的二维数值模拟

 对高温火团引发的氢气-空气混合气的瞬态爆轰过程进行了二维数值模拟,考虑了H₂-O₂-N₂的详细化学反应动力学机理,该机理包含了19个基元反应和9种组分。采用分裂格式处理带化学反应的Euler方程,其中使用全耦合的TVD格式求解流场,使用基于Gear算法的微分方程解法器求解化学反应过程。计算结果表明：在H₂∶O₂∶N₂＝0.4∶0.4∶0.2（摩尔比）的混合气中,高温气团初始温度为T/T₀=5.3时可诱导爆轰,爆轰波以2 300 m/s的速度传播,同时爆轰波阵面在管壁会形成反射波。还对计算的爆轰波后组分的浓度和温度进行了讨论,为理解爆轰波后结构提供信息。     

Influence of Small Xe Additives on the Detonation Threshold for O<Subscript>2</Subscript>−H<Subscript>2</Subscript>−He Mixtures

The effect of a small Xe additive on the conditions of detonation initiation in incident shock waves of various intensities is studied. The experiments are carried out on a shock tube facility with 10% H₂ + 5% O₂ + 85% He, 10% H₂ + 5% O₂ + 84.75% He + 0.25% Xe, and 10% H₂ + 5% O₂ + 84.5% He + 0.5% Xe mixtures. The addition of Xe led to a shift in the detonation threshold toward weaker shock waves. This effect is probably due to a significant increase in the frequency of high-energy collisions between O₂ and Xe molecules in the shock wave front in comparison with that characteristic of the equilibrium behind the wave, a factor that significantly accelerates the chemical reaction between O₂ and H₂ behind the front. The effect is a consequence of the formation of a specific translational nonequilibrium in the wave front. A previously performed numerical study of the distributions of pairs of O₂ and Xe molecules in the shock wave front shows that this effect can be enhanced by decreasing the Xe concentration from 0.5 to 0.25%. The experiment performed indirectly confirms this conclusion. It turns out that, for the mixture with 0.25% Xe, the detonation threshold shifts more strongly to the region of weaker shock waves than for the mixture with 0.5% Xe. This result gives additional arguments in favor of the assumption that this effect is due to the specifics of the translational nonequilibrium in the wave front.     

Numerical study of self-sustained oblique detonation in a non-uniform mixture

Self-sustained oblique detonation behind a spherical projectile formed in a non-uniform H₂/O₂/Ar mixture was numerically investigated. A hypersonic combustible mixture flow around a 4.76 mm diameter body was modeled to be flowing at 2500 m/s and 100 kPa. The concentration gradient was prescribed applying the Gaussian distribution to hydrogen concentration. Axisymmetric Euler equations including a detailed kinetics of 9 species and 27 elementary reactions were solved with an explicit 2nd-order time integration scheme combined with point implicit method for chemical reaction. Oblique detonation was always obtained when the mixture on the centerline was stoichiometric, as it is for a uniform mixture, and a broader range of equivalence ratio could sustain oblique detonation far from the sphere. Local detonation angle was revealed to reasonably match Chapman-Jouguet analytical solutions with a minor difference attributed to curvature, less reactive composition, and the concentration gradient. Also, a strongly fuel-rich region encountered decoupling of the shock-flame, in which an abrupt deflection of the shock front appeared. These decoupling phenomena can be attributed to a slower kinetics of a less reactive mixture. All of interesting findings in this study will also benefit understanding of various form of detonation in non-uniform mixture taking advantage of the analogy between them.     

Experimental investigation and numerical validation of explosion suppression by inert particles in large-scale duct

A large-scale duct with an explosion suppressor was designed to investigate experimentally the explosion suppression by inert particles for a CH₄/O₂/N₂ mixture. The duct is 25 m long and has an internal diameter of 700 mm. Pressure and flame signals were recorded some distance away from ignitor in the duct. Pressure tracking lines of the shock front for the different inert particle cloud densities and the inert particle diameters were made. The measured results indicate that the shock front is decoupled from the flame front in the inert particle cloud, which leads to a suppression of explosion. Also, the experiments suggest that increasing the inert particle cloud density or decreasing the inert particle diameter can enhance the ability to suppress explosion. For the purpose of validation, a two-dimensional numerical model coupled with the element chemical reaction mechanism for the simulations of the CH₄/O₂/N₂ mixture explosion suppression by the inert particles has been developed. This model makes use of the second-order TVD scheme and the MacCormack scheme to calculate gas-phase and particle-phase equations, respectively. The Strang splitting technique is used to treat the stiffness due to the coupling of the governing equations, while the implicit Gear algorithm is used to treat the stiffness due to the chemical reactions. The effect of inert particle cloud density on explosion suppression was investigated using the model. The calculated results indicate that the accumulation of inert particles slows the propagation of the gas-phase shock front and results in explosion suppression. With increased inert particle cloud density, the explosion suppression is more prominent. The calculated results show a qualitative agreement with the measured results in the large-scale duct experiment.     

Spontaneous initiation and development of hydrogen–oxygen detonation with ozone sensitization

This work studies numerically the spontaneous initiation and sustenance of a detonation wave from a hot spot with a nonuniform initial temperature embedded within an H₂O₂ mixture with and without O₃ addition. For the case with either no or just a small amount of O₃ addition, a weak reaction wave is auto-ignited at the hot spot, accelerates and then transitions to a pulsating detonation, which propagates along the temperature gradient and quenches as it runs into the cold fresh mixture. However, with increasing O₃ addition, the possibility of sustenance of a developing detonation within the gradient is significantly enhanced as it enters the cold mixture. Furthermore, the reduced induction time by O₃ addition leads to earlier appearance of the spontaneous reaction wave and detonation formation in the cold mixture, demonstrating that quenching of the detonation is largely related to the instability property of the mixture because the shortened induction time reduces substantially the instability. It is also noted that, for 5%O₃ addition, a low-temperature flame produced by the O₃ reactions is present in front of the spontaneous reaction wave, inducing a local pressure wave, which facilitates spontaneous initiation and sustains the detonation entering the cold mixture. Moreover, O₃ addition renders the critical temperature to induce the minimum spontaneous wave speed higher than the crossover temperature, while they are very close for the case without O₃.     

Comprehensive visualization of detonation-diffraction structures and sizes in unstable and stable mixtures

The geometry and characteristic length of diffraction and re-initiation during a two-dimensional detonation propagation were revealed by visualization. C₂H₄ + 3O₂ (unstable), 2C₂H₂ + 5O₂ + 7Ar (stable) and 2C₂H₂ + 5O₂ + 21Ar (stable) were used as the test mixtures. Experiments were performed over the deviation angle range from 30° to 150° and the initial pressure range from 15.8 to 102.3 kPa. By self-emitting photography, we confirmed that the geometry and the characteristic length of diffraction are not different among test gases, with the exception of the fan-like structure of re-initiation that occurred regardless of whether the mixture was unstable or stable. We conducted a compensative experiment by changing the deviation angle and initial pressure, and summarized the detonation diffraction by shadowgraph. At deviation angles larger than 60°, we measured the distances from the vertex of the channel corner to the point where the transverse detonation wave reflected on the under wall (= wall reflection distance) and confirmed that wall reflection distances are approximately in the range of 10–15 times the cell width, whether the mixture is unstable or stable.     

Critical condition of inner cylinder radius for sustaining rotating detonation waves in rotating detonation engine thruster

We describe the critical condition necessary for the inner cylinder radius of a rotating detonation engine (RDE) used for in-space rocket propulsion to sustain adequate thruster performance. Using gaseous C₂H₄ and O₂ as the propellant, we measured thrust and impulse of the RDE experimentally, varying in the inner cylinder radius r_i from 31 mm (typical annular configuration) to 0 (no-inner-cylinder configuration), while keeping the outer cylinder radius (r_o = 39 mm) and propellant injector position (r_inj = 35 mm) constant. In the experiments, we also performed high-speed imaging of self-luminescence in the combustion chamber and engine plume. In the case of relatively large inner cylinder radii (r_i = 23 and 31 mm), rotating detonation waves in the combustion chamber attached to the inner cylinder surface, whereas for relatively small inner cylinder radii (r_i = 0, 9, and 15 mm), rotating detonation waves were observed to detach from the inner cylinder surface. In these small inner radii cases, strong chemical luminescence was observed in the plume, probably due to the existence of soot. On the other hand, for cases where r_i = 15, 23, and 31 mm, the specific impulses were greater than 80% of the ideal value at correct expansion. Meanwhile, for cases r_i = 0 and 9 mm, the specific impulses were below 80% of the ideal expansion value. This was considered to be due to the imperfect detonation combustion (deflagration combustion) observed in small inner cylinder radius cases. Our results suggest that in our experimental conditions, r_i = 15 mm was close to the critical condition for sustaining rotating detonation in a suitable state for efficient thrust generation. This condition in the inner cylinder radius corresponds to a condition in the reduced unburned layer height of 4.5–6.5.     

Front shock behavior of stable curved detonation waves in rectangular-cross-section curved channels

The propagation of curved detonation waves of gaseous explosives stabilized in rectangular-cross-section curved channels is investigated. Three types of stoichiometric test gases, C₂H₄ + 3O₂, 2H₂ + O₂, and 2C₂H₂ + 5O₂ + 7Ar, are evaluated. The ratio of the inner radius of the curved channel (r_i) to the normal detonation cell width (λ) is an important factor in stabilizing curved detonation waves. The lower boundary of stabilization is around r_i/λ = 23, regardless of the test gas. The stabilized curved detonation waves eventually attain a specific curved shape as they propagate through the curved channels. The specific curved shapes of stabilized curved detonation waves are approximately formulated, and the normal detonation velocity (D_n)?curvature (κ) relations are evaluated. The D_n nondimensionalized by the Chapman–Jouguet (CJ) detonation velocity (D_CJ) is a function of the κ nondimensionalized by λ. The D_n/D_CJ?λκ relation does not depend on the type of test gas. The propagation behavior of the stabilized curved detonation waves is controlled by the D_n/D_CJ?λκ relation. Due to this propagation characteristic, the fully-developed, stabilized curved detonation waves propagate through the curved channels while maintaining a specific curved shape with a constant angular velocity. Self-similarity is seen in the front shock shapes of the stabilized curved detonation waves with the same r_i/λ, regardless of the curved channel and test gas.     

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.     

Initiation of combustion of a methane-air mixture in a supersonic flow behind a shock wave during laser excitation of O<Subscript>2</Subscript> molecules

The possibility of initiating detonation of CH₄ + air in a supersonic flow behind an oblique shock wave under the exposure of the mixture to laser radiation with wavelengths λ_I=1.268 μm and 762 nm is analyzed. It is shown that this irradiation leads to excitation of O₂ molecules to the a ¹Δ_g and b ¹Σ _g ⁺ states, which intensifies the chain mechanism of combustion of CH₄/O₂ (air) mixtures. Even for a small value of the laser radiation energy absorbed by an O₂ molecule (∼0.05–0.1 eV), detonation mode of combustion in a poorly inflammable mixture such as CH₄/air can be realized at a distance of only 1 m from the primary shock wave front for relatively small values of temperature (∼1100 K) behind the front under atmospheric pressure.     

Numerical studies on autoignition and detonation development from a hot spot in hydrogen/air mixtures

Detonation development inside spark ignition engines can result in the so called super-knock with extremely high pressure oscillation above 200?atm. In this study, numerical simulations of autoignitive reaction front propagation in hydrogen/air mixtures are conducted and the detonation development regime is investigated. A hot spot with linear temperature distribution is used to induce autoignitive reaction front propagation. With the change of temperature gradient or hot spot size, three typical autoignition reaction front modes are identified: supersonic reaction front; detonation development and subsonic reaction front. The effects of initial pressure, initial temperature, fuel type and equivalence ratio on detonation development regime are examined. It is found that the detonation development regime strongly depends on mixture composition (fuel and equivalence ratio) and thermal conditions (initial pressure and temperature). Therefore, to achieve the quantitative prediction of super-knock in engines, we need use the detonation development regime for specific fuel at specific initial temperature, initial pressure, and equivalence ratio.     

Experimental characterization of RDE combustor flowfield using linear channel

An experimental study was conducted to characterize fundamental behavior of detonation waves propagating across an array of reactant jets inside a narrow channel, which simulated an unwrapped rotating detonation engine (RDE) configuration. Several key flow features in an ethylene-oxygen combustor were explored by sending detonation waves across reactant jets entering into cold bounding gas as well as hot combustion products. In this setup, ethylene and oxygen were injected separately into each recessed injector tube, while a total of 15 injectors were used to establish a partially premixed reactant jet array. The results revealed various details of transient flowfield, including a complex detonation wave front leading a curved oblique shock wave, the unsteady production of transverse waves at the edge of the reactant jets, and the onset of suppressed reactant jets re-entering the combustor following a detonation wave passage. The visualization images showed a complex, multidimensional, and highly irregular detonation wave front. It appeared non-uniform mixing of reactant jets lead to dynamic transverse wave structure. The refreshed reactant jets evolving in the wake of the detonation wave were severely distorted, indicating the effect of dynamic flowfield and rapid pressure change. The results suggest that the mixing between the fuel and oxidizer, as well as the mixing between the fresh reactants and the background products, should affect the stability of the RDE combustor processes.     

Numerical simulation of a methane-oxygen rotating detonation rocket engine

The rotating detonation engine (RDE) is an important realization of pressure gain combustion for rocket applications. The RDE system is characterized by a highly unsteady flow field, with multiple reflected pressure waves following detonation and an entrainment of partially-burnt gases in the post-detonation region. While experimental efforts have provided macroscopic properties of RDE operation, limited accessibility for optical and flow-field diagnostic equipment constrain the understanding of mechanisms that lend to wave stability, controllability, and sustainability. To this end, high-fidelity numerical simulations of a methane-oxygen rotating detonation rocket engine (RDRE) with an impinging discrete injection scheme are performed to provide detailed insight into the detonation and mixing physics and anomalous behavior within the system. Two primary detonation waves reside at a standoff distance from the base of the channel, with peak detonation heat release at approximately 10 mm from the injection plane. The high plenum pressures and micro-nozzle injector geometry contribute to fairly stiff injectors that are minimally affected by the passing detonation wave. There is no large scale circulation observed in the reactant mixing region, and the fuel distribution is asymmetric with a rich mixture attached to the inner wall of the annulus. The detonation waves’ strengths spatially fluctuate, with large variations in local wave speed and flow compression. The flow field is characterized by parasitic combustion of the fresh reactant mixture as well as post-detonation deflagration of residual gases. By the exit plane of the RDRE, approximately 95.7% of the fuel has been consumed. In this work, a detailed statistical analysis of the interaction between mixing and detonation is presented. The results highlight the merit of high-fidelity numerical studies in investigating an RDRE system and the outcomes may be used to improve its performance.     

基于基元反应模型的H2-O2-N2爆轰数值模拟

 采用12组分、23个化学反应的基元化学反应模型,用5阶加权本质无震荡格式（WENO）、3阶TVD Runge-Kutta格式,对H₂-O₂-N₂混合气体胞格爆轰进行了数值模拟。研究了一维ZND爆轰、自维持爆轰的详细结构以及三波点附近的流动结构。计算结果表明：由横波的压力可以显著促进二维爆轰波波阵面的形成;横波的运动生成三波点,三波点造成了爆轰的自维持传播。     

Intensification of shock-induced combustion by electric-discharge-excited oxygen molecules: numerical study

Mechanisms of combustion enhancement in a supersonic H₂–O₂ reactive flow behind an oblique shock wave front are investigated when vibrational and electronic states of O₂ molecule are excited by an electric discharge. The analysis is carried out on the base of updated thermally nonequilibrium kinetic model for the H₂–O₂ mixture combustion. The presence of vibrationally and electronically excited O₂ molecules in the discharge-activated oxygen flow allows to intensify the chain mechanism and to shorten significantly the induction zone length at shock-induced combustion. It makes possible, for example, to ignite the atmospheric pressure H₂–O₂ mixture at the distance shorter than 1 m behind the weak oblique shock wave at a small energy E_s = 1.2 × 10^–2 J · cm^–3 input to O₂ molecules. At higher pressure it is needed to put greater specific energy into the gas in order to ignite the mixture at appropriate distances. It is shown that excitation of O₂ molecules by electric discharge is much more effective for accelerating the hydrogen–oxygen mixture combustion than mere heating the gas.