Initiation Of Gaseous Detonations Research Articles

The Contribution of A. K. Oppenheim to Explaining the Nature of the Initiation of Gaseous Detonation in Tubes

Abstract This paper analyzes A.K. Oppenheim’s original works on the transition of deflagration to detonation and reviews them from the perspective of new numerical and experimental results recently obtained on such phenomena. Particular attention is focused on processes happening in the boundary layer of the tube walls ahead of the accelerating flame. The results of the theoretical analyses of temperature variations inside developing boundary layer are presented and compared to the temperature variation in a free stream away from the boundary layer. Analyses of temperature increase in such layers clearly indicate that the self-ignition of the mixture happens in the boundary layer ahead of the propagating flame front. New experimental results obtained recently by a research group from the A. V. Luikov Heat and Mass Transfer Institute in Minsk, Belarus, combined with previously conducted theoretical analyses and numerical simulations, show clearly and unambiguously that the origin of the “explosion in the explosion”, postulated by A. K. Oppenheim in 1966, is always responsible for the Deflagration-Detonation Transition (DDT) in gases and is located in the boundary layer ahead of the accelerating flame front.

Asymptotic Solutions of Two Fundamental Problems in Gaseous Detonations

ABSTRACT Two recent analytical results concerning i) the direct initiation of gaseous detonations in free space and ii) the deflagration to detonation transition in tubes are revisited in this article. The first problem is treated by an asymptotic analysis in the limit of small heat release, enlightening the mechanisms controlling the direct initiation process of real detonations. The second one is limited to a one-dimensional mechanism of transition at work on the tip of elongated flames in tubes. Particular attention is paid to the physical mechanisms more than to the technical details of the analyses. However, the mathematical formulation as well as the different steps of the analysis are clearly presented in a synthetic manner.*

Analytical study of the direct initiation of gaseous detonations for small heat release

An analysis of the direct initiation of gaseous detonations in a spherical geometry is presented. The full set of constitutive equations is analysed by an asymptotic analysis in the double limit of Mach number close to unity (small heat release) and large thermal sensitivity. The quasi-steady curvature-induced quenching phenomenon is first revisited in this limit. Considering a realistic decrease rate of the rarefaction wave, the unsteady problem is reduced to a single nonlinear hyperbolic equation. The time-dependent velocity of the lead shock is an eigenfunction of the problem when two boundary conditions are imposed to the flow at the lead shock and at the burnt gas side. Following (Linan et al. , C. R. Mec. , vol. 340, 2012, pp. 829–844), the boundary condition in the quasi-transonic flow of burnt gas is expressed in terms of the curvature. Focusing our attention on successful initiation, the time-dependent velocity of the lead shock of a detonation approaching the Chapman–Jouguet regime is the solution of a nonlinear integral equation investigated for stable and marginally unstable detonations. By comparison with the quasi-steady trajectories in the phase space ‘propagation velocity versus radius’, the solution exhibits the unsteady effect produced upon the detonation decay by the long time delay of the upstream-running mode for transferring the rarefaction-wave-induced deceleration across the inner detonation structure from the burnt gas to the lead shock. In addition, a new and intriguing phenomenon concerning pulsating detonations is described. Even if the results are not quantitatively accurate, they are qualitatively relevant for real detonations.

Assessment and Control of Detonation Hazard of Silane-Containing Mixtures

A formula for calculating the induction period of a silane–air gas mixture has been proposed. The dimension of a detonation cell and the energy of direct initiation of gaseous detonation were assessed. Consideration has been given to the issue of control of the parameters of detonation of silane-containing mixtures. The parameters of Chapman–Jouguet detonation, the relative dimension of the cell of a detonation wave, and also the parameters of explosion at constant pressure and volume in a stoichiometric silane–air gas mixture with additions of chemically inert microparticles (Al2O3) have been calculated. A series of experiments was conducted on measurement of the pressure profile resulting from the explosion of the silane–air mixture in a volume of cubic shape with the known average fuel–oxidant ratio. The distribution of the fuel during the silane jet flowing out into this volume was visualized. The distribution of silane in a cloud in its outflow into the cubically shaped volume and in a high-speed jet flowing out into an unbounded space was calculated. The performed investigations can be useful in evaluating the comparative efficiency of explosion of clouds of silane– and hydrocarbon–air mixtures.

The role of multidimensional instabilities in direct initiation of gaseous detonations in free space

We numerically investigate the direct initiation of detonations driven by the propagation of a blast wave into a unconfined gaseous combustible mixture to study the role played by multidimensional instabilities in direct initiation of stable and unstable detonations. To this end, we first model the dynamics of unsteady propagation of detonation using the one-dimensional compressible Euler equations with a one-step chemical reaction model and cylindrical geometrical source terms. Subsequently, we use two-dimensional compressible Euler equations with just the chemical reaction source term to directly model cylindrical detonations. The one-dimensional results suggest that there are three regimes in the direct initiation for stable detonations, that the critical energy for mildly unstable detonations is not unique, and that highly unstable detonations are not self-sustainable. These phenomena agree well with one-dimensional theories and computations available in the literature. However, our two-dimensional results indicate that one-dimensional approaches are valid only for stable detonations. In mildly and highly unstable detonations, one-dimensional approaches break down because they cannot take the effects and interactions of multidimensional instabilities into account. In fact, instabilities generated in multidimensional settings yield the formation of strong transverse waves that, on one hand, increase the risk of failure of the detonation and, on the other hand, lead to the initiation of local over-driven detonations that enhance the overall self-sustainability of the global process. The competition between these two possible outcomes plays an important role in the direct initiation of detonations.

Prechamber Initiation of Gaseous Detonation in a Channel

ABSTRACTDeflagration-to-detonation transition in propane-butane-oxygen mixtures, in an open channel with a circular cross section with a diameter of 3 mm, was investigated experimentally. Detonation initiation was carried out by burning the mixture in the prechamber connected to the channel. To measure the velocity of a flame front, photodiodes installed along the axis of the channel were used. To determine the boundary conditions at the entrance to the channel, a piezoelectric pressure transducer was used. The influence of the dimensions of the prechamber and equivalence ratio on the pressure profile, and evolution of the flame front along the axis of the channel are presented. Effect of the prechamber detonation initiation in the channel has been analyzed. It was shown that the dynamics of the flame front and shock waves in the channel can occur in different scenarios depending on the geometry of the prechamber and equivalence ratio. The pre-detonation distances were determined.

Volumetric initiation of gaseous detonation by radiant heating of suspended microparticles

The concept of detonation wave initiation in the local volume of a fuel–gas mixture containing suspended chemically neutral microparticles heated by radiant energy from an external source is proposed. Mechanisms of initiation of the combustion and detonation waves in a region of accumulation of the radiation- heated microparticles have been studied by numerical simulation methods. Criteria that determine geometric dimensions of a region of the two-phase medium, which are necessary for the initiation of detonation waves, are formulated.

Direct initiation of gaseous detonation via radiative heating of microparticles volumetrically suspended in the gas

We propose a new conceptual approach for direct detonation initiation in the gaseous mixtures seeded with micro particles via the radiative heating from the external energy source. The basic mechanisms of energy absorption, ignition and detonation formation are analyzed numerically on the example of hydrogen-oxygen mixture. Obtained data is very promising and allows us to formulate conditions for the source power to ignite detonation in certain system geometry.

Measurement and relationship between critical tube diameter and critical energy for direct blast initiation of gaseous detonations

For the explosion safety assessment in industrial setting, detonation dynamic parameters provide important information on the sensitivity and conditions whereby detonations can be favorably occurred. In this study, new measurement of the critical tube diameter and the critical energy for direct initiation of a detonation is reported for a number of hydrocarbon–oxygen mixtures. The simultaneous experimental measurement carried out in this work allows the investigation of the direct scaling between these two dynamic parameter quantities of gaseous detonations. Using the new set of data, this paper also assesses the validity of an existing semi-empirical initiation model, namely, the surface energy model by Lee, and a simplified work done model. Both phenomenological models provide a general relationship between the two dynamic detonation parameters and comparison shows a good agreement between the theoretical results and the experimental measurement. The scaling of critical tube diameter with detonation cell size in this study also confirms the results in the previous literature.

Measurement and scaling analysis of critical energy for direct initiation of gaseous detonations

In this paper, the critical energies required for direct initiation of spherical detonations in four gaseous fuels (C2H2, C2H4, C3H8 and H2)–oxygen mixtures at different initial pressures, equivalence ratios and with different amounts of argon dilution are reported. Using these data, a scaling analysis is performed based on two main parameters of the problem: the explosion length R o that characterizes the blast wave and a characteristic chemical length that characterizes the detonation. For all the undiluted mixtures considered in this study, it is found that the relationship is closely given by $${R_{\rm o} \approx 26 \lambda}$$ , where λ is the characteristic detonation cell size of the explosive mixture. While for C2H2–2.5O2 mixtures highly diluted with argon, in which cellular instabilities are shown to play a minor role on the detonation propagation, the proportionality factor increases to 37.3, 47 and 54.8 for 50, 65 and 70% argon dilution, respectively. Using the ZND induction length Δ I as the characteristic chemical length scale for argon diluted or ‘stable’ mixtures, the explosion length is also found to scale adequately with $${R_{\rm o} \approx 2320 \Delta_I}$$ .

Reducing the critical pressure of detonation initiation in transmission to a semiconfined volume

The classical methods of initiating detonation in a volume of a reacting mixture have been studied in sufficient detail but they are not always suitable for practical purposes. This paper studies the effect of different stages of the deflagration-to-detonation transition in a small-diameter tube on the efficiency of initiation of gaseous detonation in transmission to a semiconfined volume. The methods of initiation described in this paper are important for assessing the risk of fire and explosion in household use and especially in industries.

Initiation of gaseous detonation in tubes with sharp U-bends

Initiation of gaseous detonation in tubes with sharp U-bends

Initiation of Gaseous Detonation by a Traveling Forced Ignition Pulse

Initiation of Gaseous Detonation by a Traveling Forced Ignition Pulse

An experimental investigation of the direct initiation of cylindrical detonations

The direct initiation of gaseous detonation is investigated experimentally in the cylindrical geometry. By using a long source of energy deposition along a line (i.e. pentaerythritoltetranitrate (PETN) detonating cord), undesirable charge initiation and confinement effects are eliminated. This permitted the different flow fields of direct initiation of detonation to be studied unambiguously. Although the detonation velocity in the detonating cord is finite, it was sufficiently large compared to the acoustic velocity in the surrounding gas to permit the different flow fields to be investigated within the hypersonic analogy framework, by which the detonating cord synchronizes a continuous series of cylindrical initiation events along its length. The hypersonic approximation was validated in experiments conducted in a non-reactive medium (air). In the supercritical regime of initiation in combustible gas, stable oblique detonations were observed, confirming their existence and stability. In the critical regime, the onset of detonation was observed to occur consistently from stochastic detonative centres. These centres appeared during the initial decay of the blast wave to sub-Chapman–Jouguet (CJ) velocities. The photographic evidence revealed the three-dimensional details of the detonation kernels' amplification. The present results in the cylindrical geometry are further used to discuss criteria for direct initiation of detonations. In conjunction with previous experiments in the spherical and planar geometries, a criterion for direct initiation is found to involve a critical decay rate of the reacting blast wave. In light of the experimental evidence of the inherent three-dimensional effects during the initiation phase, the strict one-dimensionality of current theoretical models is discussed.

Hot spot ignition: the Newtonian limit

One-dimensional initiation of gaseous detonations is analysed for a confined domain in which there is a prescribed thermal gradient. For this type of non-uniformity, the high-temperature regions lead to local hot spots that preferentially promote ignition. Spatio-temporal development of the hot spots, which generate complex structures within the induction domain, is governed by Clarke9s equation. In this paper, the ignition onset is studied through a combination of high activation energy asymptotics and the Newtonian limit γ → 1, where γ is an effective specific heat ratio. Examination of the hot spot behaviour reveals the existence of a region that is exponentially thin with respect to γ → 1, and it is in this region that a reaction front is born. The front is associated with a spatially evolving logarithmic singularity that corresponds to the local ignition time. Although the front decelerates rapidly as it crosses the exponentially thin zone away from the initiating hot spot, its speed remains supersonic. Explicit results for the flow field and for the singularity path are obtained; they agree well with full numerical calculations.

The role of unsteadiness in direct initiation of gaseous detonations

An analytical model is presented for the direct initiation of gaseous detonations by a blast wave. For stable or weakly unstable mixtures, numerical simulations of the spherical direct initiation event and local analysis of the one-dimensional unsteady reaction zone structure identify a competition between heat release, wave front curvature and unsteadiness. The primary failure mechanism is found to be unsteadiness in the induction zone arising from the deceleration of the wave front. The quasi-steady assumption is thus shown to be incorrect for direct initiation. The numerical simulations also suggest a non-uniqueness of critical energy in some cases, and the model developed here is an attempt to explain the lower critical energy only. A critical shock decay rate is determined in terms of the other fundamental dynamic parameters of the detonation wave, and hence this model is referred to as the critical decay rate (CDR) model. The local analysis is validated by integration of reaction-zone structure equations with real gas kinetics and prescribed unsteadiness. The CDR model is then applied to the global initiation problem to produce an analytical equation for the critical energy. Unlike previous phenomenological models of the critical energy, this equation is not dependent on other experimentally determined parameters and for evaluation requires only an appropriate reaction mechanism for the given gas mixture. For different fuel–oxidizer mixtures, it is found to give agreement with experimental data to within an order of magnitude.

Diffraction estimate of the critical energy for initiation of gaseous detonation

A criterion for the excitation of detonation is proposed: the critical initiation energy equals the work performed by the expanding detonation products along a path length equal to the longitudinal dimension of a cell. The initial radius of the layer is chosen to be equal to the radius of the detonation wave diffracted at 90° edge at the time the axial rarefaction wave converges on the axis of the gaseous charge. Formulas are obtained for estimating the critical energy for initiation of plane, cylindrical, and spherical detonation waves. The calculated values are in good agreement with experiment.

Initiation of cylindrical detonation by rapid energy deposition along a line

Initiation of gaseous detonation in hydrogen, ethylene, and acetylene-air mixtures by a line source of condensed explosives (detonating cord) is investigated experimentally. Initiation in the cylindrical geometry is important in validating a general theory of initiation and has particular significance to the interaction of high-velocity projectiles with combustible gas. The flowfields generated by the detonating cord resemble the flows observed around blunt hypersonic projectiles in combustible gas, with oblique detonation being observed in good agreement with theoretical predictions. When the energy of the detonating cord greatly exceeds the critical energy per unit length to initiate a cylindrical detonation, the blast wave generated by the cord decays monotonically to the Chapman-Jouguet (CJ) detonation speed. As the source energy approaches the critical energy predicted by theoretical models of initiation, the results become increasingly complex. In these cases, the blast wave and combustion front first decay to sub-CJ velocity, then exhibit oscillations before the final onset of detonation. The initiation of gaseous detonation is also no longer sequential along the length of the cord and is instead associated with discrete explosion centers. This phenomenon is similar to what has been previously observed in spherical initiation, suggesting a universal mechanism of detonation initiation.

Direct Initiation of Gascous Detonations

A theoretical analysis of the direct initiation of gaseous detonations by an energy source has been published recently, the results are recalled here. Nonlinear curvature effects are proved to be essential mechanisms controlling the critical condition. These effects are first studied in a quasi-steady (q-s) state approximation valid for a characteristic time scale much larger than the reaction time scale. Two branches of q-s solutions are exhibited with a C-shaped curve and a critical radius below which generalised Chapman-Jouguet (CJ) solutions cannot exist. At ordinary conditions this critical radius is much larger than the thickness of the plane CJ detonation front (typically 300 to 500 times larger). Direct numerical simulations show that the upper branch of q-s solutions, acts as an attractor of the unsteady blast waves originating from a sufficiently strong energy source. The criterion of initiation derived here works to a good approximation and exhibits the huge numerical factor (10 6 -10 8 ) which is observed in the experimental data of the critical energy source and which was not explained up to now. Transient may induce additional failure mechanisms close to the critical condition.

Initiation of gaseous detonation by a high speed body

The investigation of detonation initiated by the passage of a high speed body is presented. The following experiments are carried out for mixture of C2H2 + 2.5 O2 passed by a hemispherical or blunt cylinder with velocity ranging from 800 to 1400 m/s. A new mechanism of the transformation of shock waves to detonation waves is observed at near-critical regimes. The analytical correlation between the aerodynamical characteristics of high speed body and the physico-chemical parameters of explosive mixture is proposed as the initiation criterion of gaseous detonation. Analytical and experimental data agree well with each other.