Matei I. Radulescu

The failure mechanism of gaseous detonations: Experiments in porous wall tubes

Abstract To clarify the important role of the transverse wave structure in real detonations, we conducted experiments in porous wall tubes, as to attenuate the detonation’s transverse waves. Flow visualization and measurements of the attenuation and failure processes for three typical unstable mixtures (oxy-acetylene, oxy-methane, and oxy-propane mixtures), characterized by their highly irregular frontal structure, revealed the ongoing competition between transverse wave elimination at the porous wall and re-amplification of triple points within the reaction zone. At critical conditions, when these two effects balance, a unique failure limit is found, namely d∗ ≈ 4λ. Below this limit, the detonations fail. These experiments thus illustrate that transverse wave interactions are essential in the ignition and propagation mechanism for such unstable detonations. In comparison, experiments with argon-diluted detonations displaying a regular cellular structure with weaker transverse waves indicate that their transverse waves do not play a significant role in their propagation mechanism. The failure of these stable detonations is due to the global curvature mechanism caused by the mass divergence into the porous wall, leading to the slow distribution of frontal curvature. The results obtained in diluted and undiluted mixtures are also compared with a model taking into account the mass divergence at the permeable tube walls. Very good agreement is found for the argon-diluted mixtures, while the agreement for the unstable mixtures is very poor. This further indicates that the weak transverse wave structure in argon-diluted detonations, unlike the undiluted ones, does not significantly contribute to the ignition mechanism. Hence these argon-diluted detonations can be well approximated by a ZND reaction zone structure.

Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations

To understand the nonlinear dynamical behaviour of a one-dimensional pulsating detonation, results obtained from numerical simulations of the Euler equations with simple one-step Arrhenius kinetics are analysed using basic nonlinear dynamics and chaos theory. To illustrate the transition pattern from a simple harmonic limit-cycle to a more complex irregular oscillation, a bifurcation diagram is constructed from the computational results. Evidence suggests that the route to higher instability modes may follow closely the Feigenbaum scenario of a period-doubling cascade observed in many generic nonlinear systems. Analysis of the one-dimensional pulsating detonation shows that the Feigenbaum number, defined as the ratio of intervals between successive bifurcations, appears to be in reasonable agreement with the universal value of d = 4.669. Using the concept of the largest Lyapunov exponent, the existence of chaos in a one-dimensional unsteady detonation is demonstrated.

Numerical investigation of the instability for one-dimensional Chapman–Jouguet detonations with chain-branching kinetics

The dynamics of one-dimensional Chapman–Jouguet detonations driven by chain-branching kinetics is studied using numerical simulations. The chemical kinetic model is based on a two-step reaction mechanism, consisting of a thermally neutral induction step followed by a main reaction layer, both governed by Arrhenius kinetics. Results are in agreement with previous studies that detonations become unstable when the induction zone dominates over the main reaction layer. To study the nonlinear dynamics, a bifurcation diagram is constructed from the computational results. Similar to previous results obtained with a single-step Arrhenius rate law, it is shown that the route to higher instability follows the Feigenbaum route of a period-doubling cascade. The corresponding Feigenbaum number, defined as the ratio of intervals between successive bifurcations, appears to be close to the universal value of 4.669. The present parametric analysis determines quantitatively the relevant non-dimensional parameter χ, defined as the activation energy for the induction process ϵ I multiplied by the ratio of the induction length Δ I to the reaction length Δ R . The reaction length Δ R is estimated by the inverse of the maximum thermicity (1/ max) multiplied by the Chapman–Jouguet particle velocity u CJ . An attempt is made to provide a physical explanation of this stability parameter from the coherence concept. A series of computations is carried out to obtain the neutral stability curve for one-dimensional detonation waves over a wide range of chemical parameters for the model. These results are compared with those obtained from numerical simulations using detailed chemistry for some common gaseous combustible mixtures.

The transient start of supersonic jets

This study investigates the initial transient hydrodynamic evolution of highly under-expanded slit and round jets. A closed-form analytic similarity solution is derived for the temporal evolution of temperature, pressure and density at the jet head for vanishing diffusive fluxes, generalizing a previous model of Chekmarev using Chernyis boundary-layer method for hypersonic flows. Two-dimensional numerical simulations were also performed to investigate the flow field during the initial stages over distances of ∼ 1000 orifice radii. The parameters used in the simulations correspond to the release of pressurized hydrogen gas into ambient air, with pressure ratios varying between approximately 100 and 1000. The simulations confirm the similarity laws derived theoretically and indicate that the head of the jet is laminar at early stages, while complex acoustic instabilities are established at the sides of the jet, involving shock interactions within the vortex rings, in good agreement with previous experimental findings. Very good agreement is found between the present model, the numerical simulations and previous experimental results obtained for both slit and round jets during the transient establishment of the jet. Criteria for Rayleigh-Taylor instability of the decelerating density gradients at the jet head are also derived, as well as the formulation of a model addressing the ignition of unsteady expanding diffusive layers formed during the sudden release of reactive gases.

The effect of argon dilution on the stability of acetylene/oxygen detonations

Experimental observations indicate that dilutions with large amounts of argon lead to stable detonations having a regular cellular structure with only weak transverse waves. In the present study, the stabilizing effect of argon dilution in acetylene/oxygen detonations is investigated numerically by detailed numerical simulations of one-dimensional time-dependent pulsating detonations with a realistic seven-step chemistry model. The results show that heavy argon dilution in the mixture leads to single-frequency small-amplitude regular oscillations of the shock front pressure. As the dilution is decreased, the detonations become unstable, characterized by larger amplitude oscillations. The stabilizing role of argon is further investigated by analyzing the reaction zone structure of the steady Zeldovich-Von Neumann-Doring detonation with varying degrees of argon dilution. For the same characteristic induction lengths, the dilution with argon leads to lower temperatures in the reaction zone and slower exothermic reaction rates, thus rendering the reaction zone structure less temperature sensitive and more stable to hydrodynamic fluctuations. The present unsteady numerical simulations also indicate that with argon dilution less than approximately70%, a one-dimensional time-dependent detonation cannot self-propagate. Below this limit, due to the low-velocity excursions of the pulsating leading shock, the reactions are quenched and detonation failure occurs. This fundamental limit reveals that a one-dimensional shock-induced ignition mechanism in an unstable detonation is insufficient to account for the ignition and propagation mechanism in multidimensional detonations. These observations are consistent with recent experiments performed in porous wall tubes where, as the transverse waves were eliminated, the detonation could not self-sustain in the one-dimensional limit. The experimental stability limit, at which the transverse waves begin to play the dominant role, also corresponding to the loss of regularity in the cellular pattern, agrees very well with the stability limit determined numerically in the present study.

The mechanism of detonation attenuation by a porous medium and its subsequent re-initiation

The attenuation and re-initiation mechanism of detonations transmitted through a porous section consisting of a two-dimensional array of staggered cylinders was investigated experimentally and numerically for acetylene–oxygen mixtures. It was found that the leading order attenuation mechanism is the wave diffraction around the cylinders. The local re-amplification permitting the self-propagation of the wave was due to wave reflections from adjacent obstacles. The critical conditions for transmittance of a detonation wave were found to correspond approximately to a pore size equal to approximately 30–60 detonation induction lengths, or one to two cell sizes. For quenched detonations, the re-initiation mechanism was found to rely on wave reflections from neighbouring pores. Depending on the mixture sensitivity, one or several shock reflections may be necessary to re-amplify the attenuated detonation wave back to a self-sustained wave. For the latter case, a novel mechanism was identified, where each shock reflection gives rise to a significant enhancement of the gas reactivity and burnout of large portions of unreacted gas. This leads to a slow acceleration of the leading front, punctuated by small-scale local sudden re-accelerations. The resulting wave interactions give rise to a topologically complex reaction zone structure consisting of alternating layers of reacted and unreacted gas. The role of turbulent diffusive burning during this transient is discussed.

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.

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 Ficketts 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.

In-situ measurements of the onset of bulk exothermicity in shock initiation of reactive powder mixtures

The shock initiation process was directly observed in different powder mixtures that produce little or no gas upon reaction. The samples of reactive powder were contained in recovery capsules that permitted the samples to be analyzed after being shocked and that allowed the initiation of reaction to be monitored using three different methods. The microsecond time-scale processes were observed via a fast two-color pyrometer. Light intensity detected from the bottom of reactive samples was slightly greater compared to inert simulants in the first 10 μs after shock arrival. However, this light was much less intense than that which would correspond to the bulk of the material reacting. Thus it seemed that only small, localized zones, or hot spots, had begun to react on a time scale of less than 30 μs. Light emissions were then recorded over longer time scales, and intense light appeared at the bottom of samples a few milliseconds to a few hundreds of milliseconds after shock arrival at the bottom of the test ...

On the explosion length invariance in direct initiation of detonation

In this paper, the critical energies required to initiate a cylindrical or spherical detonation are measured experimentally in ethylene-air mixtures at ambient conditions. These results are used to validate the critical explosion length invariance, linking the critical energies in the different geometries. For the entire range of mixtures investigated, the critical explosion length R o * was found to be invariant with geometry. The critical explosion length was found to correlate well with the cell size of the mixture, yielding R o * ≊32 λ. Measurements of the shock wave velocity in the critical regime indicated that for both spherical and cylindrical detonations, the final formation of a self-sustained detonation occurred at a radius on the order of the critical explosion length R o * , suggesting that an important length scale in the direct initiation of detonation is the explosion length. A transitional geometry between spherical and cylindrical was also investigated by using finite lengths of detonating cords for initiation. It was found that when the critical length of cord is smaller than approximately R o * , it is the total energy of the source that governs whether detonation is initiated, as in spherical initiation. However, when the length of cord is longer than R o * , detonation is governed by the energy per unit length, as in the case of cylindrical initiation. The present results are in accord with the results found by Matsui and Lee in their investigation of direct initiation of acetylene-oxygen mixtures by linear sparks, suggesting that these scaling laws are universal for both fuel oxygen and fuel-air mixtures.