A numerical study of the mechanisms of self-reignition in low-overdrive detonations

Below a threshold in overdrive, both stability analysis and numerical simulations predict that one-dimensional detonations in high activation energy mixtures behave as a chaotic sequence of failures followed by reignition. Instead, less chaotic, cellular detonations almost invariably occur in experiments. Numerical simulation, based on the Euler equations with single step chemistry, shows that a ZND detonation initially fails in that regime. The detonation splits into a weaker shock, a surface discontinuity separating reacted from unreacted fluid, and a rarefaction wave. However, the detonation is eventually reignited by the explosion of a small gas pocket, in a process reminiscent of deflagration to detonation transition. In the fluid heated by the leading shock, the chemical reaction occurs slowly at first, but becomes faster as heat is released, until the pocket explodes. Small differences in initial temperature result in large enough differences in reaction time sufficient for one pocket of fluid to explode. In two dimensions, the explosion occurs earlier because an oblique shock structure develops which unevenly heats the fluid that passes through the leading shock. Hence, pockets that underwent more heating will explode sooner. As it moves upstream, the two-dimensional explosion, meets the leading shock and the detonation quickly develops a transverse wave structure. An abridged version of this paper was presented at the 15th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Boulder, Colorado, from July 30 to August 4, 1995.     

Decoupling and recoupling of detonation waves associated with sudden expansion

Detonation propagation behavior associated with sudden expansions has been investigated both experimentally and numerically. Different mechanisms, from sustained propagation to detonation failure and reinitiation including shock and flame front decoupling and recoupling have been observed with the schlieren technique. The shock-induced flame propagation has been modeled with two-step chemistry and structured two-dimensional CFD on arbitrary geometries. The results of the numerical simulations show good correspondence to the variety of phenomena observed in experiments. Thus the numerical simulation can be used to study detonation propagation in complex geometries. It provides a tool for the design of safety devices and aids experimental investigations. Received 4 August 1995 / Accepted 25 April 1996     

The influence of cellular structure on detonation transmission

We present two-dimensional numerical simulations of the transmission of detonation from a rectangular channel into a larger volume. The simulations solve the Euler equations on a Cartesian grid using the method of Flux-Corrected Transport for the fluid equations and a two-step induction parameter model for the chemistry. We simulate detonation in a H₂/O₂/Ar mixture and use sufficient grid resolution to resolve the cellular structure of the detonation. When a planar detonation front without a resolved cellular structure expands into the larger volume, the reaction front separates from the shock front and the detonation fails. When the planar front is perturbed to induce a quasi-regular cellular structure in the detonation, it again initially begins to fail, but now the presence of the transverse waves leads to reignition of the detonation in the larger volume. The form of this reignition shows striking similarities to the reignition of detonation which has been seen experimentally in H₂/O₂ mixtures. We describe this reignition mechanism in detail, and also investigate the dependence of the reignition on the number of cells in the detonation front. An abridged version of this paper was presented at the 15th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Boulder, Colorado, from July 30 to August 4, 1995     

Analytical study of idealized two-dimensional cellular detonations

In this study, the idealized two-dimensional detonation cells were decomposed into the primary units referred to as sub-cells. Based on the theory of oblique shock waves, an analytical formula was derived to describe the relation between the Mach number ratio through triple-shock collision and the geometric properties of the cell. By applying a modified blast wave theory, an analytical model was developed to predict the propagation of detonation waves along the cell. The calculated results show that detonation wave is, first, strengthened at the beginning of the cell after triple-shock collision, and then decays till reaching the cell end. The analytical results were compared with experimental data and previous numerical results; the agreement between them appears to be good, in general. Received 13 February 2001 / Accepted 2 August 2001     

Re-initiation phenomenon of gaseous detonation induced by shock reflection

The two-dimensional, time-dependent, reactive Navier–Stokes equations including the effects of viscosity, thermal conduction and molecular diffusion were solved to reveal the wave evolution and chemical dynamics involved in the re-initiation process. The computation was performed for hydrogen–oxygen–argon mixtures at the low initial pressure (8.00 kPa), using detailed chemical reaction model. The results show that, the decoupled leading shock reflects on the right wall of the vertical branch. High temperature and pressure behind the reflected shock induce the generation of hot spots and local explosion. Therefore, the re-initiation of gaseous detonation occurs. In the re-initiation area, there exist very high OH concentration and no H ₂ concentration. However, in front of reflected shock, there exist relatively high H ₂ concentration and no OH radicals. Additionally, the shock–flame interaction induces RM instability. This results in the fast mixing between hot reacted gas mixture and the relatively cold unreacted gas mixture and accelerates the chemical reactions. However, the shock–flame interaction contributes much less to the re-initiation, in contrast with shock reflection. The transition of leading shock from regular reflection to Mach reflection happens during the re-initiation. The computed evolution of wave structures involved in the re-initiation is qualitatively agreeable with that from the experimental schlieren images.      

On stability of strong and weak reflected shocks

A time-realistic adaptive unstructured Euler code is used to demonstrate the numerical existence and investigate the stability of both weak and strong reflected shocks in regular reflection. For supersonic parallel flow in a channel, impinging on two symmetrical opposing wedges, the weak reflected configuration is insensitive to downstream pressure disturbances and therefore stable. The strong reflected shock configuration is unstable to positive perturbations in back-pressure and neutrally stable to negative perturbations. A unique -shock structure provides the transition mechanism between weak and strong reflected shock configurations. Received 6 September 1999 / Accepted 10 August 2000     

Three-dimensional propagation of the transmitted shock wave in a square cross-sectional chamber

An investigation into the three-dimensional propagation of the transmitted shock wave in a square cross-section chamber was described in this paper, and the work was carried out numerically by solving the Euler equations with a dispersion-controlled scheme. Computational images were constructed from the density distribution of the transmitted shock wave discharging from the open end of the square shock tube and compared directly with holographic interferograms available for CFD validation. Two cases of the transmitted shock wave propagating at different Mach numbers in the same geometry were simulated. A special shock reflection system near the corner of the square cross-section chamber was observed, consisting of four shock waves: the transmitted shock wave, two reflection shock waves and a Mach stem. A contact surface may appear in the four-shock system when the transmitted shock wave becomes stronger. Both the secondary shock wave and the primary vortex loop are three-dimensional in the present case due to the non-uniform flow expansion behind the transmitted shock.PACS: 43.40.Nm     

Numerical simulation of Mach reflections

In this paper, the “FLIC” difference method with triangular mesh is adopted to numerically simulate the regular and Mach reflections that occur when a shock wave pass around a wedge. The compuational result is compared with the shock tube experimental results of G. Ben-Dor and I. I. Glass. The comparison shows that the position, shape of shock wave and height of Mach stem all show a good agreement. Consequently, the “FLIC” difference method with triangular mesh is quite satisfactory in numerical simulation of the regular and Mach reflections.     

A revised three-shock solution for the Mach reflection of weak shocks (1.1<M i<1.5)

It is well known that the classical three-shock theory of von Neumann (1943) does not adequately describe the configuration of the shocks close to the triple-point of a Mach reflection of an incident shock with a Mach number less than about 1.5. The assumptions on which the three-shock theory is based have been examined and several of them are shown to be invalid. The assumption that may be of most significance is that the normal components of the flows behind the reflected and the Mach stem shocks are parallel. Dropping this assumption removes an essential equation in the three-shock solution. An alternative assumption, based on experimental observation, is that there is an approximate linear relationship between the pressure behind the reflected shock and the triple-point trajectory angle. This assumption permits a revised three-shock solution which gives results that are in agreement with experimental observations of reflections of incident shocks with Mach numbers between 1.1 and 1.5.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

不稳定性对爆轰波楔面马赫反射的影响规律研究

采用一种两步化学反应模型对胞格爆轰波的楔面马赫反射过程进行了数值研究,从而澄清和解释胞格不稳定性对马赫反射发展模式和自相似性的影响。考虑到反应欧拉方程源项的刚性问题,本文采用附加RungeKutta方法耦合非刚性对流项和刚性反应源项,对流项的离散采用五阶精度的WENO格式。计算结果表明,对于稳定胞格爆轰波而言,其马赫反射过程本质上与ZND爆轰波的马赫反射是一致的,整体上不存在自相似性,胞格不稳定性只是造成了三波点轨迹线局部小振幅的波动。在楔面顶点附近,由于马赫杆是强过驱的,爆轰波的马赫反射过程是自相似的。在远场,爆轰波马赫反射的三波点轨迹线渐近的趋向于一条直线,说明重新获得了自相似性。对于不稳定的爆轰波,由于自身的不稳定性可以与马赫反射的强度相匹配,定义其三波点的轨迹是困难的,进行自相似性分析没有意义。     

Dynamics study of detonation-wave cellular structure 1. Statistical properties of detonation wave front

We have investigated the evolution of cellular detonation-wave structure as a gaseous detonation travels along a round tube and measured cell lengths as a function of the initial pressure of the gas. We have tested acetylene-containing combustible gas mixtures with different degrees of regularity. Along with the smoked-foil technique, an emission method has been used to the measure current and average values of the detonation cell length. The method is based on the detection of an emission spectrum behind the detonation front in the spectral range corresponding to local gas temperatures that are much higher than those for the Chapman-Jouguet equilibrium condition. This technique provides quasi-continuous cell-length measurements along the normal to the detonation front over the length of several factors of ten times the tube. Our study has experimentally identified the steady states of detonation structure in round tubes, referred to here as the single detonation modes. When the state of a single mode is fully established, then both the flow structure and the energy release at detonation front develop strictly periodically along the tube at a constant frequency inversely proportional to the cell length of the mixture. The mixture regularity has had no influence on the occurrence of the detonation mode, which is defined by the value of initial pressure or the total energy release of the mixture. Outside of the pressure range where a detonation mode was most likely to occur, the detonation front is unstable and may exhibit an irregular cellular pattern. Monitoring the evolution of cells over a long distance revealed that the local gas emissivity, which is time dependent and corresponds to axial pulsations of the detonation structure, has the appearance of a superposition of separate harmonics describing the states of emissivity oscillations and cell structure of single detonation modes. Received 18 October 1999 / Accepted 10 June 2001     

Non-equilibrium model of steady detonations in aluminum particles - oxygen suspensions

Steady-state detonation regimes are studied on the basis of the mathematical model of detonation of aluminum particles in oxygen taking into account differences in velocities and temperatures of the mixture components. The final steady state is analyzed by determining the types of final singularities in the plane of relaxation parameters (the ratios of characteristic times of thermal and velocity relaxations and combustion). The regions of existence of steady-state regimes are found numerically, depending on the detonation wave velocity and relaxation parameters. Numerical illustrations of various flow types are presented, and the properties of the detonation wave structure caused by velocity nonequilibrium are examined. Qualitative agreement of data obtained with frozen relaxation parameters and their dependence on the flow parameters is shown. Received 5 July 1997 / Accepted 13 July 1998     

Behavior of detonation propagation in mixtures with concentration gradients

Behavior of detonation waves in mixtures with concentration gradients normal to the propagation direction was studied experimentally. Mixtures with various concentration gradients were formed by sliding the separation plate which divides a detonation chamber from a diffusion chamber in which a diffusion gas was initially introduced. A stoichiometric hydrogen–oxygen mixture was charged in the detonation chamber, while oxygen or nitrogen was filled in the diffusion gas chamber. Temporal concentration measurement was conducted by the infrared absorption method using ethane as alternate of oxygen. Smoked foil records show a deformation of regular diamond cells to parallelogram ones, which well corresponds to local mixture concentration. Schlieren photographs reveal the tilted wave front whose angle is consistent with the deflection angle of the detonation front obtained from trajectories of the triple point. The local deflection angle increases with increase in local concentration gradient. Calculation of wave trajectory based on the ray tracing theory predicts formation of the tilted wave front from an initial planar front.      

激波绕半菱形柱体运动的实验研究和数值模拟

激波绕过半菱形柱体流场是十分复杂的,本文用实验方法和数值模拟对该问题作了系统研究。实验是在UTIAS激波管上进行的,数值模拟采用2阶精度Godunow格式,最后实验结果和数值模拟作了比较。     

Analysis of the shock structures in a regular detonation

Time-dependent two-dimensional numerical simulations have been used to investigate the detailed shock structures and patterns of energy release in the regions of the triple points and transverse waves in a planar detonation. As the system of shock triple points evolves between collisions, they trace a well shaped cellular pattern characteristic of detonations in argon-diluted, low-pressure mixtures of hydrogen and oxygen. In the region of the triple points, the shock structure evolves continuously from a single Mach structure to a double Mach structure and finally to a complex Mach structure characteristic of spinning detonations. Most of the energy released in the region of the triple points. The amount of energy release increases as the triple point comes closer to a collision with a wall or another triple point. Just before the collision, there is a large region of energy release that covers the length of the interacting transverse waves. The result is a rectangular high-energy region which boosts the propagation of the new detonation cell.     

Three-dimensional numerical simulation of detonations in coaxial tubes

Three-dimensional numerical simulation of detonations in both a circular tube and a coaxial tube are simulated to reveal characteristics of single spinning and two-headed detonations. The numerical results show a feature of a single spinning detonation which was discovered in 1926. Transverse detonations are observed in both tubes, however, the single spinning mode maintains the complex Mach reflection whereas the two-headed mode develops periodically from the single Mach reflection to the complex one. The calculated cell aspect ratio for the two-headed mode changes from 1.09 to 1.34 as the radius of axial insert increases from r ₁/R = 0.1 to 0.9. The calculated cell aspect ratio for r ₁/R = 0.1 is close to the experimental results without an axial insert. The formation of an unreacted gas pocket behind the detonation front was not observed in the single spinning mode; however, the two-headed mode has unreacted gas pocket behind the front near the axial insert.      

Numerical simulations of shock wave reflection phenomena in non-stationary flows using regularized smoothed particle hydrodynamics (RSPH)

In this paper we wish to demonstrate to what extent the numerical method regularized smoothed particle hydrodynamics (RSPH) is capable of modelling shocks and shock reflection patterns in a satisfactory manner. The use of SPH based methods to model shock wave problems has been relatively sparse, both due to historical reasons, as the method was originally developed for studies of astrophysical gas dynamics, but also due to the fact that boundary treatment in Lagrangian methods may be a difficult task. The boundary conditions have therefore been given special attention in this paper. Results presented for one quasi-stationary and three non-stationary flow tests reveal a high degree of similarity, when compared to published numerical and experimental data. The difference is found to be below 5, in the case where experimental data was found tabulated. The transition from regular reflection (RR) to Mach reflection (MR) and the opposite transition from MR to RR are studied. The results are found to be in close agreement with the results obtained from various empirical and semi-empirical formulas published in the literature. A convergence test shows a convergence rate slightly steeper than linear, comparable to what is found for other numerical methods when shocks are involved.     

A numerical simulation of reflection processes of a detonation wave on a wedge

Abstract. A two dimensional numerical simulation has been performed to study reflection processes of detonation waves on a wedge. The numerical scheme adopted is the flux corrected transport scheme and a two-step chemical reaction is assumed for a stoichiometric oxyhydrogen mixture diluted with argon. Transverse wave structures of the detonation are produced by artificial disturbances situated in front of a one-dimensional Chapman-Jouguet detonation wave. Numerical grids are generated by solving a Laplace equation. Results show that in the case where Mach reflection occurs, the cells in the Mach stem are smaller than those in the incident wave and are distorted in shape. There is also an initiating stage during which the cells in the Mach stem are created. The critical angle beyond which Mach reflection cannot occur is discussed. Received 15 October 1999 / Accepted 27 March 2000     

Experimental and numerical studies on interactions of a spherical flame with incident and reflected shocks

Observations are presented from experiments and calculations where a laminar spherical CH4/air flame is perturbed successively by incident and reflected shock waves. The experiments are performed in a standard shock tube arrangement, in which a high-speed shadowgraph imaging system is used to record evolutions of the flame. Numerical simulations are conducted by using second-order wave propagation algorithms, based on two-dimensional axisymmetric Navier-Stokes equations with detailed chemical reactions. Qualitative agreements are obtained between the experimental and numerical results. Under actions of incident shock waves, Richtmyer-Meshkov instability responsible for the flame deformation is induced in the flame, and the distoned flame takes a barrel shape. Then, under subsequent actions of the shock wave reflected from a planar wall, the flame takes an inclined non-symmetrical kidney shape in a symmetric cross section, which means a mushroom-like shape of the flame comes finally into being. The vorticity direction in the ring cap has been altered by the reflected shock＇s action, which makes the head of the mushroom-like flame extend quickly to the side wall.