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     

Direct initiation of detonations in unconfined gasoline sprays

Large scale experiments on detonation initiation in gasoline-air by two different sources were carried out at stoichiometric conditions. Unconfined clouds of volume generated by a special facility had a shape of semicylinder of 15–17 m in length and 6–8 m in radius. Both the charge of condensed HE and the charge of stoichiometric propane-air were used to initiate detonation in the mixture. In case of initiation by a propane-air charge the critical initiation energy was up to 7 times as large as that for HE initiation. The detonation cell size for gasoline-air was determined as 0.04–0.05 m. It was shown, that the well-known correlation between the critical energy of point blast initiation and the cell size failed for this system. The cell size obtained is close to one of propane-air, but no direct transfer of detonation from one mixture to another was observed. Received 10 March 1995 / Accepted 12 March 1995     

Critical reactions for the hydrazine vapor detonations

A detailed kinetic model devoted to the hydrazine vapor detonation has been built. It consists of 33 reversible reactions and 13 species. A reduced kinetic model has been proposed by using the Principal Component Analysis of matrix F (PCAF) method as implemented in KINALC. It is constituted of 26 reactions and 11 species. This model has been shown to be valid over a pressure range of 0.1 to 10 atm. However, the predictions of the models are significantly affected by changes in the enthalpy of formation of NH. With the help of the full kinetic model, a value of A, the proportionality factor in the ZND model between the induction distance in the detonation wave and the detonation cell size, of has been derived if one considers that the collision efficiency of NH on the thermal decomposition of hydrazine is equal to the one of N. The value of A for pure hydrazine detonation is shown to be strongly dependent on the value of the collision efficiency of NH. Received 24 December 2000 / Accepted 11 April 2001     

Recent work on gaseous detonations

The paper reviews recent progress in the field of gaseous detonations, with sections on shock diffraction and reflection, the transition to detonation, hybrid, spherically-imploding, and galloping and stuttering fronts, their structure, their transmission and quenching by additives, the critical energy for initiation and detonation of more unusual fuels. The final section points out areas where our understanding is still far from being complete and contains some suggestions of ways in which progress might be made. Received 9 September 1999 / Accepted 10 May 2001     

Fundamentals of rotating detonations

A rotating detonation propagating at nearly Chapman–Jouguet velocity is numerically stabilized on a two-dimensional simple chemistry flow model. Under purely axial injection of a combustible mixture from the head end of a toroidal section of coaxial cylinders, the rotating detonation is proven to give no average angular momentum at any cross section, giving an axial flow. The detonation wavelet connected with an oblique shock wave ensuing to the downstream has a feature of unconfined detonation, causing a deficit in its propagation velocity. Due to Kelvin–Helmholtz instability existing on the interface of an injected combustible, unburnt gas pockets are formed to enter the junction between the detonation and oblique shock waves, generating strong explosions propagating to both directions. Calculated specific impulse is as high as 4,700 s.      

Effect of scale on the onset of detonations

Critical conditions for onset of detonations are compared at (1) two significantly different scales, (2) for a range of -air mixtures diluted with C, O, and (3) for two types of geometry – one a long obstructed channel and the other a room with a relatively small aspect ratios. For the range of scales, mixtures, and initial conditions tested, the detonation cell size was shown to be a reliable scaling parameter for characterization of detonation onset conditions. An experimental correlation is suggested for the critical detonation onset conditions. This correlation is based on a wide variety of available experimental data on DDT in mixtures of hydrogen and hydrocarbon fuels with air and on the use of detonation cell size as a scaling parameter characterizing the mixture. Received 14 November 1999 / Accepted 16 February 2000     

Reignition of detonations by reflected shocks

Numerical simulations are used to study the diffraction, decay, and reignition that occurs when a detonation propagates past an increase in cross-sectional area in a rectangular tube. The computations solve the time-dependent two-dimensional equations describing a reactive flow in an argon-diluted stoichiometric hydrogen-oxygen mixture at atmospheric pressure. Previous studies have shown that soon after transmission to a larger area, the reaction front decouples from the leading shock and forms a decaying blast wave (“bubble”) in the larger tube. Then, depending on the initial conditions, the detonation either continues to decay or is reignited as the bubble reflects off confining surfaces. For a strongly overdriven initiating detonation, reignition occurs through an interaction between the bubble and the original contact surface. For a more weakly driven system, reignition can occur in two ways: either in the slip line and Mach stem of the Mach reflection formed when the bubble reflects off the bottom surface of the tube, or by multiple shock interactions that occur when the reflected bubble overtakes the initial detonation front. The computations show the evolution and development of the cellular structure of the steady detonation front. Submitted to the 14th International Colloquium on the Dynamics of Energetic and Reactive Systems, Coimbra, Portugal, August, 1993     

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     

Dynamics of oblique detonations in ram accelerators

Time-accurate numerical simulations are used to study the dynamic development of oblique detonations on accelerating projectiles in ram accelerators. These simulations show that the oblique detonation can be stabilized on the projectile. The high pressure generated behind the detonation can result in accelerations up to 10⁶G and propel the projectile to velocities higher than 4.0 km/s. The detonation structure on the projectile is sensitive to the projectile geometry. A small change in the projectile shape is sufficient to alter the overall detonation structure and significantly affect the pressure distribution on the projectile. In order to maximize the thrust, an appropriate projectile shape has to be chosen to generate the detonation structure just behind the widest part of the projectile body. The projectile acceleration also has strong effects on the flow field and the detonation structure. During the acceleration, the location of the oblique detonation moves upstream from one reflected shock to another. However, one the detonation is stabilized behind the upstream shock, it remains at the new location until the transition to the next upstream shock occurs. In the simulations, the Non-Inertial-Source (NIS) technique was used to accurately represent of the projectile acceleration. Also, the Virtual-Cell-Embedding (VCE) method was employed to efficiently treat the complex projectile geometry on cartesian grids.     

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     

Propagation of nitromethane detonations in porous media

The characteristics of the propagation of a detonation in chemically sensitized nitromethane in a dense porous medium are investigated. By introducing liquid NM+15% (by weight) DETA into densely packed beds of solid spherical glass beads 66μm to 2.4 mm in diameter, a highly heterogeneous explosive mixture is obtained. The critical (i.e., failure) charge diameter of this mixture is systematically measured in unconfined charges over a wide range of bead sizes. Velocity measurements are also made for the various charges. It is found that there exists a critical bead size above which the critical diameter decreases with increasing bead size and below which it decreases with decreasing bead size. This result indicates an abrupt change in the mechanism of propagation at the critical bead size. Velocity measurements further support this by emphasizing the different behavior above and below the critical point.     

The influence of detonation cell size and regularity on the propagation of gaseous detonations in granular materials

This paper presents results from an experimental study of transmission of gaseous detonation waves through various granular filters. Spherical glass beads of 4 and 8 mm diameter and crushed rock of 7.5 mm volume averaged diameter were used as filter material. Varying the initial pressure of the detonating gas mixture controlled the detonation cell size. Dilution with argon was used to vary the detonation cell regularity. The complete range from almost no detonation velocity deficit to complete extinction of the combustion wave was observed. The existing correlation for gaseous detonation velocity deficit where is the critical diameter for the gaseous detonation and is the pore size, is found to be applicable for both smooth spherical particles and irregular crushed rock when considering irregular detonation structures. Soot films and pressure measurements show that as the detonation cell size is increased, reinitiation of a reanular filter until it finally no longer occurs at . Complete extinction of the combustion wave occurs at . These two limits appear to be about the same for irregular and regular detonation cell structures. For irregular structures without argon dilution, can be found for detonation wave failure, and can be found for complete extinction of the combustion wave. For argon dilution these limits are changed to and , respectively. The data are a bit scarce as a basis for proposing a new correlation for regular structures, but as a first approximation log is suggested for regular structures. The detonation or combustion wave is found to approach a constant velocity in the granular filter if not extinguished. Received 31 October 2001 / Accepted 15 July 2002 Published online 4 November 2002 Correspondence to: T. Slungaard (e-mail: slung@maskin.ntnu.no) 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     

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.     

Two-dimensional numerical simulations of multi-headed detonations in oxygen-aluminum mixtures using an adaptive mesh refinement

Abstract. Two-dimensional numerical simulations of detonations in two-phase lean mixtures of aluminum particles and pure oxygen have been performed. The computational procedure adopts an adaptive mesh refinement methodology in order to increase spatial resolution in the most interesting parts of the flow field. A one-step heterogeneous reaction describes the evaporation and combustion of aluminum. Depending on the gas-phase temperature, the combustion product is aluminum oxide or aluminum monoxide. The results show that the heterogeneous detonations resemble gaseous single-phase ones although the scale of the phenomena is very different. The detonation of aluminum dust evolves into the 2-headed mode of propagation with the characteristic detonation cell width equal to cm. For aluminum dust the cellular structure is much finer. The detonation initially propagates in the 11-headed mode with the characteristic cell width equal to cm and evolves into the 8.5-headed mode with the characteristic cell size $\lambda_{\rm cell}$ equal to cm. Received 7 May 2001 / Accepted 25 March 2002 Published online 23 January 2003 Correspondence to: K. Benkiewicz (e-mail: kbenk@cow.me.aoyama.ac.jp)     

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     

Numerical predictions of oblique detonation stability boundaries

Oblique detonation stability was studied by numerically integrating the two-dimensional, one-step reactive Euler equations in a generalized, curvilinear coordinate system. The integration was accomplished using the Roe scheme combined with fractional stepping; nonlinear flux limiting was used to prevent unphysical solution oscillations near discontinuities. The method was verified on one- and two-dimensional flows with exact solutions, and its ability to correctly predict one-dimensional detonation stability boundaries was demonstrated. The behavior of straight oblique detonations attached to curved walls was then considered. Using the exact, steady oblique detonation solution as an initial condition, the numerical simulation predicted both steady and unsteady oblique detonation solutions when a detonation parameter known as the normal overdrive, , was varied. For a standard test case with a specific heat ratio of , a dimensionless activation energy of , and dimensionless heat release of , an oblique detonation with a constant dimensionless component of velocity tangent to the lead shock, , underwent transition to unstable behavior at . This is slightly higher than the threshold of predicted by one-dimensional theory; thus, the two-dimensionality renders the flow slightly more susceptible to instability. Received 4 August 1996 / Accepted 5 March 1996     

Symplectic analysis for wave propagation in one-dimensional nonlinear periodic structures

The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.     

Comparison of critical conditions for DDT in regular and irregular cellular detonation systems

Abstract. The results of an experimental study of DDT in mixtures with regular and irregular detonation cellular structures are presented. Experiments were carried out in a tube 174 mm i. d. with obstacles (blockage ratios were 0.1, 0.3, and 0.6). Mixtures used were hydrogen–air and stoichiometric hydrogen–oxygen diluted with , Ar, and He. The critical conditions for DDT are shown to depend on the regularity of the cellular structure of test mixtures. The critical values of the cell sizes in Ar- and He-diluted mixtures are shown to be significantly smaller than those in -diluted mixtures. This means that systems with a highly regular detonation cellular structure have far less capacity for undergoing DDT compared to irregular ones with the same values of detonation cell sizes. Received 18 November 1999 / Accepted 15 May 2000