Investigation of counter-rotating shock wave phenomenon and instability mechanisms of rotating detonation engine with hollow combustor and Laval nozzle

The counter-rotating shock wave phenomenon and instability mechanisms in the hollow rotating detonation combustor with a Laval nozzle are investigated. The in-house solver BYRFoam based on the OpenFOAM platform and the detailed chemical reaction kinetic mechanism are used. The coupling of the detonation wave and the shock wave is revealed, with the continuous presence of the counter-rotating shock wave in the combustor that propagates in the opposite direction to the detonation wave and oscillates in intensity. The intensities of both the detonation wave and the counter-rotating shock wave are found to be constantly oscillating, and this instability is referred to as the collision-oscillation instability. It is caused by the complex interaction between the detonation wave, the fresh gas and the counter-rotating shock wave. The velocity difference between the detonation wave and the counter-rotating shock wave is found to lead to the migration of the collision point, which in turn leads to the peak periodic undulation phenomenon of the pressure curve, that is, the wave packet. This instability is called the counter-rotating instability, which co-exists with the collision-oscillation instability for a long time. The results of this study are compared with the experimental data, and the reasons for the oscillation of the experimental pressure signal are explained.     

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.     

Numerical investigation of two-wave collision and wave structure evolution of rotating detonation engine with hollow combustor

A three-dimensional numerical simulation of rotating detonation engine (RDE) with hollow combustor is performed to analyze wave structure evolution systematically. Wave structure evolution is classified into four categories, namely two-wave collision (counter-rotating waves), abscission of detonation tail, and shock wave to detonation transition. Two-wave collision consists of symmetric detonation collision, asymmetric detonation collision, and detonation/shock collision. Two symmetric detonation waves turn into shock waves after collision. Collision of asymmetric detonation waves creates single detonation wave. The detonation/shock collision decreases the detonation wave intensity. Abscission of detonation tail and shock to detonation transition can both create single detonation wave or two opposite-direction detonation waves, depending on the wave hitting angle and the amount of fresh gas. All phenomena mentioned above affect the number of detonation waves in the combustion chamber.     

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.     

Formation and evolution of two-dimensional cellular detonations

This paper reports the results of numerical simulations of cellular detonations generated by using numerical noise as a source of initial fluctuations imposed on a strong planar shock propagating through the reactive medium. The calculations show that a plane detonation wave moving at Chapman-Jouguet (CJ) velocity is unstable to transverse perturbations with wavelength greater than one or two half-reaction-zone lengths. The numerical noise affects the initial cell formation process, but it has no influence on the cell size and regularity of the structures developed. Increasing the activation energy results in more irregular structures characterized by stronger triple points, larger variations of the local shock velocity inside the detonation cell, and higher frequency of appearance and disappearance of triple points. These features of the systems with irregular cellular structures can account for the experimental observation that such systems are less affected by boundary conditions. For the two-dimensional detonation, the average reaction zone is larger and maximum reaction rate is lower than in the one-dimensional case. This means that the formation of detonation cells reduces the maximum entropy production in the reaction zone, and slows down the approach of the system to the equilibrium state. This effect is shown to increase with activation energy due to larger unreacted gas pockets, and deeper penetration of the pockets into the region of mostly burned material.     

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...     

Numerical investigation of pre-detonator in rotating detonation engine

Pre-detonators are commonly used in rotating detonation engine (RDE) experiments. Current experimental studies focus on the performance of pre-detonator while ignoring the influence of pre-detonator on the flow field. In numerical simulations one-dimensional detonation wave is usually used to ignite the fresh gas in RDE. This is a simplification of the pre-detonator used in practical hotfire tests. But the coupling between the pre-detonator and the combustor is ignored. The aim of the present study is to study the influence of pre-detonator on the flow field in the RDE. A model of RDE with a pre-detonator is built, in which three-dimensional numerical simulations fueled with hydrogen/air is performed. The influence of pre-detonator on the combustor in different stages is studied. After initiation, detonation wave from the pre-detonator forms two counter-rotating detonation waves. The tangential installation of pre-detonator fails in directional initiation of detonation wave. The coupling effect is shown as the reflection and expulsion of shock wave. Detonation wave or oblique shock wave in the combustion chamber enters the pre-detonator and turns into shock wave before colliding with the end and re-entering the combustion chamber. Under some circumstances, the reflected shock wave will initiate a detonation wave and affect the wave structure in the combustion chamber. In the stable stage, the reflected shock wave has no effect on the flow field. However, periodic collision of reflected shock wave with detonation wave at the junction causes ablation in long-time experiments. Increasing the axial distance between pre-detonator and injection wall is expected to be a solution for the ablation problem.     

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.”     

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.     

Experimental study on the detonation propagation behaviors through a small-bore orifice plate in hydrogen-air mixtures

In this study, the regimes of detonation transmission through a single orifice plate were investigated systematically in a 6-m length and 90-mm inner diameter round tube. A series of experiments on the detonation propagation mechanisms in hydrogen-air mixtures were performed. A single obstacle with different orifice size (d) from 10 to 60 mm was adopted to study the effects of the induced perturbations on the detonation propagation. Here, the thickness of orifice plate (δ) was fixed at 10.33 mm. Detonation velocity was determined from the time-of-arrival (TOA) of the detonation wave recorded by eight high-speed piezoelectric pressure transducers (PCB102B06). Detonation cellular size was obtained by the smoked foil technique. The characteristic of detonation velocity evolution were quantitatively analyzed after it passes through a single obstacle, and particular attention was paid to the cases for which the blockage ratio (BR) is greater than 0.9, i.e., the cases of small hole diameter of d < 25 mm. The experimental results showed that, in a smooth tube, only super-critical condition and sub-critical condition can be observed. After the orifice plate is introduced into the tube, critical condition occurs. The detonation re-initiation with distinct cellular structures was experimentally observed. Of note is that when the blockage ratio (BR) values in the range of 0.802–0.96, it was easier to detonate at the fuel-lean side. Finally, the critical condition for detonation propagation through an orifice plate was quantified as d/λ > 1 where λ is the detonation cell size.     

On the dynamic detonation parameters in acetylene–oxygen mixtures with varying amount of argon dilution

In this investigation, the dynamic detonation parameters for stoichiometric acetylene–oxygen mixtures diluted with varying amount of argon are measured and analyzed. The experimental results show that the critical tube diameter and the critical energy for direct initiation of spherical detonations increase with the increase of argon dilution. The scaling behavior between the critical tube diameter d_c and the detonation cell size λ as well as the critical direct initiation energy E_c is systematically studied with the effect of argon dilution. The present results again validate that the relation d_c = 13λ holds for 0–30% argon diluted mixtures and breaks down when argon dilution increases up to 40%. It is found that the explosion length scaling of R_o ∼ 26λ becomes also invalid when the mixture contains approximately this same amount of argon dilution or more. This critical argon dilution is indeed close to that found from experiments in porous-walled tubes by Radulescu and Lee (2002) which exhibit a distinct transition in the failure mechanism. Cell size analysis in literature also indicates that the cellular detonation front starts to become more regular (or stable) when the argon dilution reaches more than 40–50%. Regardless of the degree of argon dilution or mixture sensitivity, the phenomenological model developed from the surface energy concept by Lee, which provides a relation that links the critical tube diameter and the critical energy remains valid. The present experimental results also follow qualitatively the observation from chemical kinetic and detonation instability analyses.     

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.     

Assessment of H2-CH4-air mixtures oxidation kinetic models used in combustion

Because of a wide number of applications, the potential hazards of H₂-CH₄-air mixtures have to be characterised. For hazard evaluation, an important element is a reliable detailed kinetic scheme. In the present study, three modern kinetic models, those of Konnov, of Dagaut and the GRI-mech 03, have been evaluated with respect to a large set of experimental data, including species profiles obtained in jet-stirred reactor, laminar flame speed, ignition delay time and detonation cell size, for hydrogen-methane-air mixtures. For jet-stirred reactor data, the model of Dagaut provides significantly better results. For flame speed data modeling, the three models are as reliable. For ignition delay times, the model of Dagaut seems the most reliable. For detonation cell size predictions, the model of Konnov is the best. Important chemical reactions are underlined through sensitivity and reaction pathway analysis and are discussed in the frame of rate constant values recommended by Baulch et al.     

Effect of multi-bend geometry on deflagration to detonation transition of a hydrocarbon-air mixture in tubes

We present a numerical investigation of gaseous deflagration-to-detonation transition (DDT) triggered by a shock in a multi-bend geometry. The ethylene-air mixture filled rigid tube with obstacles is considered for understanding the effects of complex confinement and initial flame size on DDT. Our calculations show generation of hot spots by flame and strong shock interactions, and flame propagation is either restrained or accelerated due to the wall obstacles of both straight and bent tubes. The effect of initial flame size on DDT in complex confinement geometry is analyzed as well as the hot spot formation on promoting shock–flame interaction, leading to a full detonation.     

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.     

Effect of perforated plate with high blockage rate on detonation re-initiation in H2–O2-Ar mixture

An experimental investigation was performed to study the pressure limits and mechanism of the detonation re-initiation behind the perforated plate with various thicknesses and hole diameters in H₂–O₂-Ar mixture by schlieren and soot track measurement. The Chapman-Jouguet (CJ) detonation and overdriven detonation were used to collide with the perforated plate. For the CJ detonation transmission, the detonation re-initiation distance is larger than 3.9 times the tube hydraulic diameter. Both the thickness and the hole size have significant effects on the critical pressure and the re-initiation distance. The ratios of the hole hydraulic diameter and the critical cell size ($d_H/{\lambda }_c$) are less than 1. The cellular structure can be observed near the perforated plate on the smoked foils due to the collision of the arc-sharp shock waves via multi-jet structure. For the overdriven detonation transmission, the detonation can be re-initiated quickly, and the re-initiation distances are all less than twice the tube hydraulic diameter. The re-initiation distance increases with the hole size while the thickness has little effect on the re-initiation distance. The “abrupt” mode of the detonation re-initiation is transformed into the “gradual” mode with the increase of the initial pressure. The pressure limit of the re-initiation mode transformation also increases with the decrease of the hole size. Two mechanisms of the multi-jet initiation: rapid turbulent mixing initiation and the induction by the collisions of transverse waves were verified experimentally, corresponding to the “abrupt” and “gradual” modes, respectively. The critical condition of detonation propagation can be quantified as d_H/λ¹ > 3.37 and 3.77 for the 3 mm-hole and 2 mm-hole perforated plates, respectively, where d_H is the hydraulic diameter and λ is the detonation cell size.     

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.     

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.     

A comprehensive skeletal mechanism for the oxidation of n-heptane generated by chemistry-guided reduction

Applied to the primary reference fuel n-heptane, we present the chemistry-guided reduction (CGR) formalism for generating kinetic hydrocarbon oxidation models. The approach is based on chemical lumping and species removal with the necessity analysis method, a combined reaction flow and sensitivity analysis. Independent of the fuel size, the CGR formalism generates very compact submodels for the alkane low-temperature oxidation and provides a general concept for the development of compact oxidation models for large model fuel components such as n-decane and n-tetradecane. A defined sequence of simplification steps, consisting of the compilation of a compact detailed chemical model, the application of linear chemical lumping, and finally species removal based on species necessity values, allows a significantly increased degree of reduction compared to the simple application of the necessity analysis, previously published species, or reaction removal methods. The skeletal model derived by this procedure consists of 110 species and 1170 forward and backward reactions and is validated against the full range of combustion conditions including low and high temperatures, fuel-lean and fuel-rich mixtures, pressures between 1 and 40 bar, and local (species concentration profiles in flames, plug flow and jet-stirred reactors, and reaction sensitivity coefficients) and global parameters (ignition delay times in shock tube experiments, ignition timing in a HCCI engine, and flame speeds). The species removal is based on calculations using a minimum number of parameter configurations, but complemented by a very broad parameter variation in the process of compiling the kinetic input data. We further demonstrate that the inclusion of sensitivity coefficients in the validation process allows efficient control of the reduction process. Additionally, a compact high-temperature n-heptane oxidation model of 47 species and 468 reactions was generated by the application of necessity analysis to the skeletal mechanism.     

Shock-to-detonation transition of nitromethane: Time-resolved emission spectroscopy measurements

The objective of this work is to improve the knowledge of the shock-to-detonation transition of nitromethane. The study is based on a spectral analysis in the range 0.3–0.85 μm, with a 28-nm resolution, during experiments of plane shock impacts on explosive targets at 8.6 GPa. The time-resolved radiant spectra show that the detonation front, the reaction products produced during the superdetonation, and the detonation products are semitransparent. The temperature and absorption coefficient profiles are determined from the measured spectra by a mathematical inversion method based on the equation of radiative transfer with Rayleigh scattering regime. Shocked nitromethane reaches at least 2500 K, showing the existence of local chemical reactions after shock entrance. Levels of temperature of superdetonation and steady-state detonation are also determined.