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.     

Formation of transverse waves in oblique detonations

The structure of oblique detonation waves stabilized on a hypersonic wedge in mixtures characterized by a large activation energy is investigated via steady method of characteristics (MoC) calculations and unsteady computational flowfield simulations. The steady MoC solutions show that, after the transition from shock-induced combustion to an overdriven oblique detonation, the shock and reaction complex exhibit a spatial oscillation. The degree of overdrive required to suppress this oscillation was found to be nearly equal to the overdrive required to force a one-dimensional piston-driven detonation to be stable, demonstrating the equivalence of two-dimensional steady oblique detonations and one-dimensional unsteady detonations. Full unsteady computational simulations of the flowfield using an adaptive refinement scheme showed that these spatial oscillations are transient in nature, evolving in time into transverse waves on the leading shock front. The formation of left-running transverse waves (facing upstream) precedes the formation of right-running transverse waves (facing downstream). Both sets of waves are convected downstream away from the wedge in the supersonic flow behind the leading oblique front, such that the mechanism of instability must continuously generate new transverse waves from an initially uniform flow. Together, these waves define a cellular structure that is qualitatively similar to a normal propagating detonation.     

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.     

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.     

Studies on the valveless scheme to produce high-frequency detonations with different purge methods

Producing high-frequency detonations is an important topic for pulse detonations which has received considerable attentions. The valveless scheme has been verified to be able to obtain high-frequency detonations more than 100 Hz. This work has been conducted to investigate the possibility to achieve a higher detonation frequency and clarify the limits of stable operations preliminarily for the valveless scheme with different purge methods. Oxygen, ethylene, and nitrogen or liquid water are utilized as oxidizer, fuel, and purge medium in the experiments while two injection configurations are employed. The maximum detonation frequencies of 180 Hz and 330 Hz have been achieved in stable operations for two different injection configurations when nitrogen is used as the purge gas. The ceiling frequency for stable detonations is 300 Hz if nitrogen is replaced by liquid water, which indicates that water vapor is capable to create an efficient buffer zone to ensure stable operations. The results imply that the injection configuration also has a great impact on the ceiling stable detonation frequency. Three operating modes have been observed in this study, i.e., a stable detonation mode, an unstable detonation mode, and a deflagration mode. In the unstable mode, failure of detonation initiation occurs frequently and one interesting phenomenon is that the detonation frequency is reduced by half exactly when insufficient filling happens. The supply pressure ratios of oxidizer to fuel and purge to fuel are obtained for different operating modes when the purge method is changed. Furthermore, the equivalence ratios have been also studied for different operating modes which reveals that the range will change when different purge methods and injection configurations are employed. According to the equivalence ratio and the mass flow rates, an equivalent volume fraction of oxygen is defined and its range for the stable detonation mode is clarified.     

Numerical study of three-dimensional detonation wave dynamics in a circular tube

The three-dimensional structures of a detonation wave propagating in a circular tube were investigated using a one-step irreversible Arrhenius kinetics model. A series of parametric studies were carried out to investigate the different modes of cell structure formation by changing the pre-exponential factor. Maximum pressure trace was recorded along the tube wall to investigate the detonation cell structures. The unsteady results obtained in three dimensions revealed the generation mechanism of the wave front structures of two-, three- and four-cell mode detonations. A six-cell mode detonation could be obtained using a finer grid. With the increase in pre-exponential factor, it was found that the number of detonation cells is increased while the cell size is reduced accordingly. In all the multi-cell modes, the detonation wave structures and smoked-foil records on the wall are formed by the propagation of transverse waves along the wall in clockwise and counter-clockwise directions, while the slapping wave moves in the radial direction. The presence of the slapping wave further strengthens the wave interactions in three-dimensional simulation. Comparison with two-dimensional simulation confirms the effect of the slapping wave in the radial direction. As a result, the detonation wave front structures changes from the polygonal shape to the multi-bladed fan shape, periodically.     

Mach reflection bifurcations as a mechanism of cell multiplication in gaseous detonations

Detonation waves in gases are unstable and form cellular structures. The cellular structure can range from being very regular, to very irregular, where new modes are continuously formed on the front of the detonation wave. The present work addresses the mechanism of new cell formation in irregular structure detonations. Using idealized one-step chemistry calculations on sufficiently wide domains, as to avoid mode-locking, the present work reveals a novel mechanism for new mode formation in cellular detonations. The mechanism involves the creation of wave bifurcations on the front of the Mach shock following triple shock collisions. The numerical simulations reveal that these new triple points, through further reflections with pre-existing modes in asymmetric cells, can give rise to cell multiplication. Parameters favourable to this mechanism were found in good correlation with parameters leading to irregular cellular structures, as observed in previous experiments.     

一维爆轰波在扰动来流中传播的数值研究

爆轰波在静止气体或定常来流中的传播得到了广泛研究, 然而在扰动来流中的传播研究较少。这方面的研究不仅是爆轰传播机制的重要组成部分, 还可为爆轰发动机的应用提供参考。文章基于两步诱导-放热总包反应模型, 开展了一维爆轰波在正弦密度扰动来流中的传播数值模拟。通过对数值结果分析, 获得了放热反应控制参数与爆轰波内在不稳定性的关系, 并在此基础上研究了扰动波长和幅值对一维爆轰波动力学过程的影响。研究发现, 在波前施加连续扰动会诱导爆轰波表现出更复杂的动力学行为, 且影响过程与爆轰波的内在不稳定性相关。对于稳定爆轰波, 扰动只在特定波长范围内引起前导激波后的压力振荡。对于不稳定爆轰波, 扰动会进一步强化其内在不稳定性。扰动幅值越大, 对爆轰波动力学过程的影响越显著。      

Structural characteristics of detonation expansion from a small channel to a larger one

We report on numerical simulations of the evolution of two-dimensional detonation waves that are expanded from a small channel to a larger one. In accordance with experimental data, the simulations predict three different types of evolution, namely, supercritical, critical and subcritical detonations. In a supercritical detonation, the reaction zone remains always attached to the precursor shock, whereas in a critical one it temporarily detaches and then re-attaches to the front. In the subcritical type, the extinction is permanent, i.e., the detonation quenches. The effects of the fuel’s activation energy and the channel-width ratio are studied via a parametric study. It is found that sufficiently large values of these two parameters can result to flows of the critical and even the subcritical type. Finally, three-dimensional simulations have also been performed and are briefly discussed herein.     

Nonlinear dynamics of self-sustained supersonic reaction waves: Fickett's detonation analogue

The present study investigates the spatiotemporal variability in the dynamics of self-sustained supersonic reaction waves propagating through an excitable medium. The model is an extension of Fickett's detonation model with a state-dependent energy addition term. Stable and pulsating supersonic waves are predicted. With increasing sensitivity of the reaction rate, the reaction wave transits from steady propagation to stable limit cycles and eventually to chaos through the classical Feigenbaum route. The physical pulsation mechanism is explained by the coherence between internal wave motion and energy release. The results obtained clarify the physical origin of detonation wave instability in chemical detonations previously observed experimentally.     

Detonation simulations in supersonic flow under circumstances of injection and mixing

The unsteady, reactive Navier-Stokes equations with a detailed chemical mechanism of 11 species and 27 steps were employed to simulate the mixing, flame acceleration and deflagration-to-detonation transition (DDT) triggered by transverse jet obstacles. Results show that multiple transverse jet obstacles ejecting into the chamber can be used to activate DDT. But the occurrence of DDT is tremendously difficult in a non-uniform supersonic mixture so that it required several groups of transverse jets with increasing stagnation pressure. The jets introduce flow turbulence and produce oblique and bow shock waves even in an inhomogeneous supersonic mixture. The DDT is enhanced by multiple explosion points that are generated by the intense shock wave focusing of the leading flame front. It is found that the partial detonation front decouples into shock and flame, which is mainly caused by the fuel deficiency, nevertheless the decoupled shock wave is strong enough to reignite the mixture to detonation conditions. The resulting transverse wave leads to further mixing and burning of the downstream non-equilibrium chemical reaction, resulting in a high combustion temperature and intense flow instabilities. Additionally, the longitudinal and transverse gradients of the non-uniform supersonic mixture induce highly dynamic behaviors with sudden propagation speed increase and detonation front instabilities.     

Transverse wave generation mechanism in rotating detonation

Detonation engines are expected to be included in a number of aerospace thrusters in the future. Several types of detonation engines are currently under examination, including the rotating detonation engine (RDE). Although the RDE has been explored experimentally, its rotating detonation propagation mechanism is not well understood. This paper clarifies the detonation mechanism and dynamics of the RDE by 2D and 3D simulation using compressible Euler equations with a full chemical reaction mechanism of H₂/O₂ and H₂/Air, especially from the triple-point and transverse detonation points of view. A total variation diminishing (TVD) scheme is used for the mixture of H₂/Air, and an advection upwind splitting method difference vector (AUSMDV) scheme is used for the mixture of H₂/O₂. The use of an AUSMDV scheme provides a much clearer detonation structure than does the TVD scheme. We focus on the complex interaction mechanism of the detonation front and burned mixture gases. We found out that at this interaction point, an unreacted gas pocket appears and ignites periodically to generate transverse waves at the detonation front and maintain detonation propagation.     

气相爆轰波沿胞格的动力学机理研究

 建立了一种以子单元分析为基础,研究气相爆轰波沿胞格运动时的动力学机理的新方法。根据该子单元的性质和斜冲击波关系,首先推导了对撞前后前导冲击波沿胞格对称轴的马赫数之比和入射冲击波入射角及胞格几何性质的关系,求解了胞格结构中的三波点对撞问题。然后,采用爆炸波模拟前导冲击波的自持运动过程,求解气相爆轰波沿胞格的动力学过程,理论分析表明,气相爆轰波在胞格起点首先经历一个增长过程,然后才出现衰减。理论分析结果与实验和数值计算结果的比较表明符合得较好。     

Self-sustaining, weakly curved, imploding pathological detonation

We provide the first theoretical demonstration of the existence of quasi-one-dimensional, quasi-steady, self-sustaining convergent detonation waves. These occur in systems where, in the planar wave, the rate of heat release by chemical reaction reaches a maximum at a point of incomplete reaction. The case examined in the present paper is that for a two-step sequential reaction, with the second stage endothermic. We construct detonation velocity against curvature relationships for converging waves, and compare these theoretical curves with direct numerical simulations of imploding detonations in cylindrical and spherical geometries. We also comment on the one-dimensional stability of imploding and diverging detonation fronts governed by the two-step model.     

A review of direct numerical simulations of astrophysical detonations and their implications

Multi-dimensional direct numerical simulations (DNS) of astrophysical detonations in degenerate matter have revealed that the nuclear burning is typically characterized by cellular structure caused by transverse instabilities in the detonation front. Type Ia supernova modelers often use onedimensional DNS of detonations as inputs or constraints for their whole star simulations.While these one-dimensional studies are useful tools, the true nature of the detonation is multi-dimensional. The multi-dimensional structure of the burning influences the speed, stability, and the composition of the detonation and its burning products, and therefore, could have an impact on the spectra of Type Ia supernovae. Considerable effort has been expended modeling Type Ia supernovae at densities above 1×10⁷ g·cm^-3 where the complexities of turbulent burning dominate the flame propagation. However, most full star models turn the nuclear burning schemes off when the density falls below 1×10⁷ g·cm^-3 and distributed burning begins. The deflagration to detonation transition (DDT) is believed to occur at just these densities and consequently they are the densities important for studying the properties of the subsequent detonation. This work will review the status of DNS studies of detonations and their possible implications for Type Ia supernova models. It will cover the development of Detonation theory from the first simple Chapman–Jouguet (CJ) detonation models to the current models based on the time-dependent, compressible, reactive flow Euler equations of fluid dynamics.     

High resolution numerical simulation of the structure of 2-D gaseous detonations

Two dimensional numerical simulation of the structure of gaseous detonation is investigated by utilizing the single step Arrhenius kinetic reaction mechanism in both high and low activation energy mixtures, characterized by their irregular and regular detonation structure, respectively. All the computations are performed on a small Beowulf cluster with six nodes. The dependency of the structure on the grid resolution is performed and it is found that, resolution of more than 300 cells per hrl is required to demonstrate the role of hydrodynamic instabilities, (KH and RM instabilities) in detonation propagation in irregular structures, while due to the absence of fine-scale structures, resolution of 50 cells per hrl, gives the physical structure of detonation with regular structures. Results show that the transverse waves in irregular structure are significantly stronger than the transverse wave in regular structure detonation, which can enhance the burning rate of the unburned pockets behind the shock front. Results for resolution of 600 cells per hrl illustrate that, in addition to the primary mode, the interaction of large vortices with the shock front provides secondary modes in the structure which leads to the irregularity of the structure in high activation energy mixture. In contrast with the results obtained for regular structure, which no unburned gas pockets and vortices observed behind the front, the results for irregular structure reveal that most portions of the gases, escape from shock compression and create large unburned gas pockets behind the both weak section of the Mach stem and the incident wave, which will burn eventually by the turbulent mixing due to the vortices associated with hydrodynamic instabilities. Therefore, the ignition mechanism in irregular structure is due to the both shock compression and by turbulent mixing associated with hydrodynamic instabilities, while the shock compression yields the ignition mechanism in regular structure detonation.     

On the characteristics of two-dimensional double cellular detonations with two successive reactions model

Double cellular detonations were numerically investigated using two-dimensional Euler equations with two successive chemical reactions, whose reaction lengths differ one order of magnitude. Simulated soot track images showed the double cellular structure with two cell widths that differ one order of magnitude, as well as previous experiments and numerical simulations. We successfully divided the double cellular detonation with two successive exothermic reactions into two detonations, primary and secondary detonations, with a single exothermic reaction, based on p–v relation of Rayleigh line and Hugoniot curves with the addition of the hypothetical condition of intermediate initial state. The ratio of cell widths of primary and secondary detonations showed good agreement with that caused by the first and second reactions of double cellular detonation, and there was no interaction between two successive chemical reactions. The linear stability analysis of planar detonation and the soot rack images of double, primary and secondary detonations showed that instabilities of primary and secondary detonations are dominant to that of double cellular detonation with two successive reactions. We confirmed the validity of division of two successive reactions to clarify the detonation instability and its cellular structure.     

Experimental study of the relief of the front of steady detonation in liquid high explosives

The instability of detonation waves in a 81 : 19 nitromethane-acetone mixture is experimentally studied. The amplitude of the irregularities caused by detonation instability and the typical reaction time are estimated using a VISAR laser interferometer, which makes it possible to measure the particle velocity profiles at the explosive-window interface. The characteristic transverse dimensions of the irregularities are measured with the help of a CORDIN camera operating in the single shooting mode to record the intrinsic emission of the detonation front or the light of an outside source reflected from it.     

The effects of mixture preburning on detonation wave propagation

Pressure gain combustion in the form of continuous detonations can provide a significant increase in the efficiency of a variety of propulsion and energy conversion devices. In this regard, rotating detonation engines (RDEs) that utilize an azimuthally-moving detonation wave in annular systems are increasingly seen as a viable approach to realizing pressure gain combustion. However, practical RDEs that employ non-premixed fuel and oxidizer injection need to minimize losses through a number of mechanisms, including turbulence-induced shock-front variations, incomplete fuel-air mixing, and premature deflagration. In this study, a canonical stratified detonation configuration is used to understand the impact of preburning on detonation efficiency. It was found that heat release ahead of the detonation wave leads to weaker shock fronts, delayed combustion of partially-oxidized fuel-air mixture, and non-compact heat release. Furthermore, large variations in wave speeds were observed, which is consistent with wave behavior in full-scale RDEs. Peak pressures in the compression region or near triple points were considerably lower than the theoretically-predicted values for ideal detonations. Analysis of the detonation structure indicates that this deflagration process is parasitic in nature, reducing the detonation efficiency but also leading to heat release far behind the wave that cannot directly strengthen the shock wave. This parasitic combustion leads to commensal combustion (heat release far downstream of the wave), indicating that it is the root cause of combustion efficiency losses.