Modelling of detonation cellular structure in aluminium suspensions

Heterogeneous detonations involving aluminium suspensions have been studied for many years for industrial safety policies, and for military and propulsion applications. Owing to their weak detonability and to the lack of available experimental results on the detonation cellular structure, numerical simulations provide a convenient way to improve the knowledge of such detonations. One major difficulty arising in numerical study of heterogeneous detonations involving suspensions of aluminium particles in oxidizing atmospheres is the modelling of aluminium combustion. Our previous two-step model provided results on the effect on the detonation cellular structure of particle diameter and characteristic chemical lengths. In this study, a hybrid model is incorporated in the numerical code EFAE, combining both kinetic and diffusion regimes in parallel. This more realistic model provides good agreement with the previous two-step model and confirms the correlations found between the detonation cell width, and particle diameter and characteristic lengths. Moreover, the linear dependence found between the detonation cell width and the induction length remains valid with the hybrid model.     

Three-dimensional cellular structure of detonations in suspensions of aluminium particles

Recently, we have used scarce available data on the detonation cell size in suspensions of aluminium particles in air and oxygen to adjust the kinetic parameters of our two-phase model of detonations in these mixtures. The calculated detonation cell width was derived by means of two-dimensional (2D) unsteady simulations using an assumption of cylindrical symmetry of the flow in the tube. However, in reality, the detonation cells are three-dimensional (3D). In this work, we have applied the same detonation model which is based on the continuous mechanics of two-phase flows, for 3D numerical simulations of cellular detonation structures in aluminium particle suspensions in oxygen. Reasonable agreement on the detonation cell width was obtained with the aforementioned 2D results. The range of tube diameters where detonations in $\text{ Al/O}_2$ mixture at a given particle size and concentration would propagate in the spinning mode has been estimated (these results make a complement to our previous analysis of spinning detonations in Al/air mixtures). Coupling these results with the dependencies of detonation cell size on the mean particle diameter is of great interest for the understanding of fundamental mechanisms of detonation propagation in solid particle suspensions in gas and can help to better guide the experimental studies of detonations in aluminium suspensions. It is shown that the part of detonation wave energy used for transverse kinetic energy of both gas and particles is quite small, which explains why the propagation velocity of spinning and multi-headed detonations reasonably agrees with the ideal CJ values.     

Structure and stability of one-dimensional detonationsin ethylene-air mixtures

The propagation of one-dimensional detonations in ethylene-air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit, first-order-accurate, time marching algorithm. The ethylene-air combustion is modeled with a 20-species, 36-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies over an equivalence ratio range of for different initial pressures and degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel-air equivalence ratio. For equivalence ratios less than approximately 1.2 the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures ( 1.2$" align="middle" border="0"> ) exhibit a low-frequency mode that includes large fluctuations in the detonation wave speed. At high degrees of overdrive, stable detonation wave propagation is obtained. A modified McVey-Toong short-period wave-interaction theory is in excellent agreement with the numerical simulations.Received: 13 September 2004, Revised: 1 November 2004, Published online: 3 March 2005[/PUBLISHED]Correspondence to: S. Yungster     

Propagation mechanism of dust detonations

This paper summarizes the studies on dust detonations at the Stosswellenlabor of RWTH Aachen since 1987. The onset and propagation mechanism of heterogeneous dust detonations are similar to those of marginal gas phase detonations. A self-sustained dust detonation has transverse wave structures that provide the coupling between shock and reaction. Large transition distances and transverse wave spacings require large sized tubes for the propagation of self-sustained dust detonations. The Hugoniot analysis of the Chapman-Jouguet detonation predicts equilibrium detonation states being in reasonable agreement with the self-sustained dust detonations observed. Shock matching calculations at the triple point adequately determine the wave structures of those stable dust detonations.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.     

Shock and detonation wave diffraction at a sudden expansion in gas–particle mixtures

Numerical modeling of the propagation of shock and detonation waves is carried out in a duct with an abrupt expansion for a heterogeneous mixture of fine particles of aluminum and oxygen. A considerable difference from corresponding flows in pure gas is found. The influence of the size and mass loading of particles on the flow and shock wave structure behind the backward-facing step is determined. As in gaseous detonations, three types of scenarios of detonation development are obtained. Specific features of the flow structure are revealed such as deformation of the combustion front due to interaction between the relaxation zone and the vortex structure. The influence of particle size and channel width on detonation propagation is analyzed. This paper is based on work that was presented at the 21th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

DDT and detonation waves in dust-air mixtures

This paper summarizes the studies of DDT and stable detonation waves in dust-air mixtures at the Stosswellenlabor of RWTH Aachen. The DDT process and propagation mechanism for stable heterogeneous dust detonations in air are essentially the same as in the oxygen environment studied previously. The dust DDT process in tubes is composed of a reaction compression stage followed by a reaction shock stage as the pre-detonation process. The transverse waves that couple the shock wave and the chemical energy release are responsible for the propagation of a stable dust-air detonation. However, the transverse wave spacing of dust-air mixtures is much larger. Therefore, DDT and propagation of a stable detonation in most industrial and agricultural, combustible dust-air mixtures require a tube that has a large diameter between 0.1 m and 1 m and a sufficient length-diameter ratio beyond 100, when an appropriately strong initiation energy is used. Two dust detonation tubes, 0.14 m and 0.3 m in diameter, were used for observation of the above-mentioned results in cornstarch, anthraquinone and aluminum dust suspended in air. Smoked-foil technique was also used to measure the cellular structure of dust detonations in the 0.3 m detonation tube. Received 11 February 2000 / Accepted 1 August 2000     

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.      

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.     

Aluminum Particles–air Detonation at Elevated Pressures

The effect of initial pressure on aluminum particles–air detonation was experimentally investigated in a 13 m long, 80 mm diameter tube for 100 nm and 2 μm spherical particles. While the 100 nm Al–air detonation propagates at 1 atm initial pressure in the tube, transition to the 2 μm aluminum–air detonation occurs only when the initial pressure is increased to 2.5 atm. The detonation wave manifests itself in a spinning wave structure. An increase in initial pressure increases the detonation sensitivity and reduces the detonation transition distance. Global analysis suggests that the tube diameter for single-head spinning detonation or characteristic detonation cell size would be proportional to (d ₀: aluminum particle size, p ₀: initial pressure). Its application to the experimental data results in m ~ O(1) and n ~ O(1) for 1 to 2 μm aluminum–air detonation, thus indicating a strong dependence on initial pressure and gas-phase kinetics for the aluminum reaction mechanism in detonation. Hence, combustion models based on the fuel droplet diffusion theory may not be adequate in describing micrometric aluminum–air detonation initiation, transition and propagation. For 2 μm aluminum–air mixtures at 2 atm initial pressure and below, experiments show a transition to a “dust quasi-detonation” that propagates quasi-steadily with a shock velocity deficit nearly 40% with respect to the theoretical C–J detonation value. The dust quasi- detonation wave can propagate in a tube with a diameter less than 0.4–0.5 times the diameter required for a spinning detonation wave.     

Deflagration to detonation transition fueled by dust layers

The roles which dust layers play in severe dust explosions were investigated in a 70 m long and 30 cm inside diameter horizontal Flame Acceleration Tube (FAT) with one end closed and the other end open to the atmosphere. A variety of dusts such as corn dust, cornstarch, Mira Gel starch, wheat dust, and wood flour were layered on the bottom half of the FAT. To initiate the combustion process, a detonation tube filled with a stoichiometric H₂/O₂ mixture at room temperature and 1 atm pressure was used to ignite a short presuspended dust cloud with a dust concentration of 500–600 g/m³. Combustion waves generated by this dust cloud travel toward the open end of the FAT and are continuously fueled by the dust/air mixtures. Flame propagation processes in the FAT were closely monitored by a variety of measuring instruments at different locations. The study demonstrates that stable quasi-detonation were reached in some runs, but self-sustained Chapman-Jouguet detonations were not observed possibly due to the limitation of the tube length. Attempts were made to determine the structure of dust detonations fueled by a dust layer. Preliminary evidence indicates that for Mira Gel starch the leading shock is essentially a triple shock configuration which involves a Mach stem and for wheat and wood dusts there possibly exists a multi-headed spin structure.     

Investigation of detonation initiation in aluminium suspensions

Detonation initiation is investigated in aluminium/oxygen and aluminium/air mixtures. Critical conditions for initiation of spherical detonations are examined in analogy with the criteria defined for gaseous mixtures, which correlate critical parameters of detonation initiation to the characteristic size of the cellular structure. However, experimental data on the detonation cell size in these two-phase mixtures are very scarce, on account of the difficulty to perform large-scale experiments. Therefore, 2D numerical simulations of the detonation cellular structure have been undertaken, with the same combustion model for Al/air and Al/O₂ mixtures. The cell size is found to be λ = 37.5 cm for a rich (r = 1.61) aluminium–air mixture, and λ = 7.5 cm for a stoichiometric aluminium-oxygen mixture, which is in reasonable agreement with available experimental data. Calculations performed in large-scale configurations (up to 25 m in length and 1.5 m in lateral direction) suggest that the critical initiation energy and predetonation radius for direct initiation of the unconfined detonation in the aluminium–air mixture are, respectively, 10 kg of TNT and 8 m. Moreover, numerical simulations reveal that the structure of the detonation wave behind the leading front is even more complicated than in pure gaseous mixtures, due to two-phase flow effects. This paper is based on work that was presented at the 21st International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Photographic investigation into the mechanism of combustion in irregular detonation waves

Irregular detonations are supersonic combustion waves in which the inherent multi-dimensional structure is highly variable. In such waves, it is questionable whether auto-ignition induced by shock compression is the only combustion mechanism present. Through the use of high-speed schlieren and self-emitted light photography, the velocity of the different components of detonation waves in a ${\text{ CH}}_4+2\text{ O}_2$ mixture is analyzed. The observed burn-out of unreacted pockets is hypothesized to be due to turbulent combustion.     

Structure and multiplicity of detonation regimes in heterogeneous hybrid mixtures

The problem of propagation of steady nonideal detonations in heterogeneous hybrid mixtures is studied in the case of a hydrogen-air gaseous mixture with suspended fine aluminum particles. Due to the difference in the order of magnitude of the characteristic induction and combustion times of gaseous mixture and solid particles, the process of energy release behind the leading shock front occurs over an extended period of time and in a nonmonotonic way. An approximate numerical model has been improved to find the steady propagation regimes and investigate their structure. The problem is analyzed in the frame of the theory of the mechanics of multiphase media with mass, momentum and heat exchanges between particles and gases. The one-dimensional ZND model of detonation with losses to the lateral boundaries is used. It is shown that three different steady propagation regimes may exist: the Pseudo-Gas Detonation (PGD), the Single-Front Detonation (SFD) and the Double-Front Detonation (DFD). The numerical results match the available experimental results obtained previously. The influence of the fundamental parameters of the system on the domains of existence of the different regimes is displayed. Moreover, it is shown that, according to the theory of nonideal detonations with nonmonotonic energy release, there may exist a multiplicity of detonation modes. However, the total number of solutions actually obtained by numerical calculations differs from that predicted by the theory. The reasons for these discrepancies are discussed.     

大型水平爆轰管中悬浮铝粉爆炸过程的实验研究

铝粉的燃烧与爆轰性能是粉尘爆炸领域研究的热点.利用长29.6m,内径199mm,配有40套喷粉扬尘系统的水平爆轰管,在40J电火花点火条件下,实现了悬浮铝粉-空气混和物火焰加速、爆燃、爆轰及其转捩过程,测得了爆炸波传播过程中的压力信号,并且观察到了爆轰波的稳定传播现象.实验结果表明,当铝粉浓度为300 g/m3时,在距离点火端10.15m(长径比L/D=51)处发生了DDT,测得的爆轰波传播过程中管内的最大爆速为1840m/s,最大峰值超压为10.5MPa.铝粉尘爆炸波在爆轰管内的传播过程可分为爆燃段、爆燃转爆轰(DDT)、爆轰增强以及稳态爆轰四个阶段.     

粉尘火焰加速现象的实验研究

粉尘火焰的发生、加速及由爆燃向爆轰转捩的机理是个至今尚未弄清的问题。需要解决的技术关键之一是在实验室实现弱点火条件下的粉尘火焰加速直至达到爆轰状态。着手发展了一种球形喷粉扬尘装置，令产生的扬尘湍流在水平实验管中形成空间均匀分布和维持秒级悬浮的粉尘云状态。采用以上扬尘装置的水平实验管，在６ｇ黑火药的六点平面点火条件下获得了微细铝粉火焰经５ｍ长的传播过程加速至１０００ｍ／ｓ的实验结果。给出了扬尘湍流强度、粉尘粒度与浓度、点火能量及方式等因素对粉尘火焰加速过程中所起作用，及变截面效应（由小变大）对粉尘火焰减速的影响。     

The propagation mechanism of high speed turbulent deflagrations

The propagation regimes of combustion waves in a 30 cm by 30 cm square cross–sectioned tube with an obstacle array of staggered vertical cylindrical rods (with BR=0.41 and BR=0.19) are investigated. Mixtures of hydrogen, ethylene, propane, and methane with air at ambient conditions over a range of equivalence ratios are used. In contrast to the previous results obtained in circular cross–sectioned tubes, it is found that only the quasi–detonation regime and the slow turbulent deflagration regimes are observed for ethylene–air and for propane–air. The transition from the quasi–detonation regime to the slow turbulent deflagration regime occurs at (where D is the tube “diameter” and is the detonation cell size). When , the quasi–detonation velocities that are observed are similar to those in unobstructed smooth tubes. For hydrogen–air mixtures, it is found that there is a gradual transition from the quasi–detonation regime to the high speed turbulent deflagration regime. The high speed turbulent deflagration regime is also observed for methane–air mixtures near stoichiometric composition. This regime was previously interpreted as the “choking” regime in circular tubes with orifice plate obstacles. Presently, it is proposed that the propagation mechanism of these high speed turbulent deflagrations is similar to that of Chapman–Jouguet detonations and quasi-detonations. As well, it is observed that there exists unstable flame propagation at the lean limit where . The local velocity fluctuates significantly about an averaged velocity for hydrogen–air, ethylene–air, and propane–air mixtures. Unstable flame propagation is also observed for the entire range of high speed turbulent deflagrations in methane–air mixtures. It is proposed that these fluctuations are due to quenching of the combustion front due to turbulent mixing. Quenched pockets of unburned reactants are swept downstream, and the subsequent explosion serves to overdrive the combustion front. The present study indicates that the dependence on the propagation mechanisms on obstacle geometry can be exploited to elucidate the different complex mechanisms of supersonic combustion waves. Received 5 November 2001 / Accepted 12 June 2002 / Published online 4 November 2002 Correspondence to: J. Chao (e-mail: jenny.chao@mail.mcgill.ca) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001.     

Effects of nitrates on hydrocarbon-air flames and detonations

Abstract. The subject of hydrocarbon sensitization by nitrates under conditions of a heterogeneous spray has been of interest due to its applicability in promoting ignition. To gain insight into the mechanisms of the nitrate sensitization effect, the present work was limited to vapour phase studies at elevated temperatures in order to avoid the influence of heterogeneous factors. The experiments performed included studies of flammability, flame propagation, shock ignition and detonation. The mixtures used were composed of air, hexane, and isopropyl nitrate (IPN) with IPN concentrations ranging from 0 to 100 mole % in hydrocarbon-IPN. In addition, methane and propane were also included in the flame experiments. For the shock ignition and detonation experiments, the measured ignition delay and detonation cell size had minimum values for IPN-air and maximum values for hexane-air. With increases in the IPN concentration, the ignition delay and detonation cell size fell monotonically between the values for hexane and IPN. This monotonic behaviour was explained to be the result of mixing the hydrocarbon with the more sensitive nitrate whose energetics are larger than or comparable to the hydrocarbon when mixed with air. For the slow combustion mode, the results also confirmed the monotonic behavior and showed that the lean flammability limit and the flame velocity fell between those of the hydrocarbon and IPN. Received 10 September 1999 / Accepted 27 July 2000     

Cellular detonations in bidispersed gas-particle mixtures

Formation of cellular detonation in bi-fractional stoichiometric mixtures of aluminum particles and oxygen is investigated numerically. The detonation cell size depends on the particle diameters and relative concentration of the fractions. Certain degeneration of cellular detonation is obtained when compared to the monodisperse mixtures. It is characterized by maximal pressure decrease, transverse wave relaxation and detonation front rectification. Complete degeneration of cellular detonations and stable propagation of a plane detonation front is found in some bi-fractional mixtures. The numerical results are confirmed by acoustic analysis of the detonation structures. This paper is based on work that was presented at the 21st International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Wave dynamic processes in cellular detonation reflection from wedges

When the cell width of the incident detonation wave (IDW) is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H ₂/O ₂ diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes. The English text was polished by Yumming Chen.     

Combustion tube studies of dust flame acceleration

A new pneumatic dispersion system for obtaining a good quality uniform dust suspension in a horizontal dust combustion tube was developed. The effect of three different dispersion techniques on self-sustained dust flame acceleration in such a combustion tube was examined. The importance of the dispersion quality in the test tube for maintaining a self-sustained dust flame acceleration was demonstrated. A combustion tube for studies of flame acceleration in fine aluminum dust-air mixture and its transition to detonation under industrial ignition conditions was constructed in the course of the present study. It consists mainly of an initiation section and a test section. The initiation section must be equipped in a well-developed dispersion system for creating a good dispersion condition in the test tube. The length of this section is 3 meters. The test tube requires only to distribute uniformly the dust over the bottom of the tube prior to the experiment. The aluminum dust spherical in shape with 6 μm in diameter was used for tests. Experimental results demonstrated that the increase in flame velocity is roughly linear through the entire length of the test tube. The highest flame propagation velocity in fine aluminum dust-air mixture approaches some 1200m/s at a distance of 4.8m from the ignition plane.