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

A numerical study of detonation diffraction

An investigation of detonation diffraction through an abrupt area change has been carried out via a set of two-dimensional numerical simulations parameterized by the activation energy of the reactant. Our analysis is specialized to a reactive mixture with a perfect gas equation of state and a single-step reaction in the Arrhenius form. Lagrangian particles are injected into the flow as a diagnostic tool for identifying the dominant terms in the equation that describes the temperature rate of change of a fluid element, expressed in the shock-based reference system. When simplified, this equation provides insight into the competition between the energy release rate and the expansion rate behind the diffracting front. The mechanism of spontaneous generation of transverse waves along the diffracting front is carefully analysed and related to the sensitivity of the reaction rate to temperature. We study in detail three highly resolved cases of detonation diffraction that illustrate different types of behaviour, super-, sub- and near-critical diffraction

Hydrodynamic instabilities in gaseous detonations: comparison of Euler, Navier–Stokes, and large-eddy simulation

A large-eddy simulation is conducted to investigate the transient structure of an unstable detonation wave in two dimensions and the evolution of intrinsic hydrodynamic instabilities. The dependency of the detonation structure on the grid resolution is investigated, and the structures obtained by large-eddy simulation are compared with the predictions from solving the Euler and Navier–Stokes equations directly. The results indicate that to predict irregular detonation structures in agreement with experimental observations the vorticity generation and dissipation in small scale structures should be taken into account. Thus, large-eddy simulation with high grid resolution is required. In a low grid resolution scenario, in which numerical diffusion dominates, the structures obtained by solving the Euler or Navier–Stokes equations and large-eddy simulation are qualitatively similar. When high grid resolution is employed, the detonation structures obtained by solving the Euler or Navier–Stokes equations directly are roughly similar yet equally in disagreement with the experimental results. For high grid resolution, only the large-eddy simulation predicts detonation substructures correctly, a fact that is attributed to the increased dissipation provided by the subgrid scale model. Specific to the investigated configuration, major differences are observed in the occurrence of unreacted gas pockets in the high-resolution Euler and Navier–Stokes computations, which appear to be fully combusted when large-eddy simulation is employed

Ignition of Deflagration and Detonation Ahead of the Flame due to Radiative Preheating of Suspended Micro Particles

We study a flame propagating in the gaseous combustible mixture with suspended inert particles. The gas is assumed to be transparent for the radiation emitted by the combustion products, while particles absorb and re-emit the radiation. Thermal radiation heats the particles, which in turn transfer the heat to the surrounding gaseous mixture by means of heat conduction, so that the gas temperature lags that of the particles. We consider different scenarios depending on the spatial distribution of the particles, their size and the number density. In the case of uniform distribution of the particles the radiation causes a modest increase of the temperature ahead of the flame and the corresponding increase of the flame velocity. The effects of radiation preheating is stronger for a flame with smaller normal velocity. In the case of non-uniform distribution of the particles, such that the particles number density is smaller just ahead of the flame and increases in the distant region ahead of the flame, the preheating caused by the thermal radiation may trigger additional independent source of ignition. This scenario requires the formation of a temperature gradient with the maximum temperature sufficient for ignition in the region of denser particles cloud ahead of the advancing flame. Depending on the steepness of the temperature gradient formed in the unburned mixture, either deflagration or detonation can be initiated via the Zeldovich's gradient mechanism. The ignition and the resulting combustion regimes depend on the temperature profile which is formed in effect of radiation absorption and gas-dynamic expansion. In the case of coal dust flames propagating through a layered dust cloud the effect of radiation heat transfer can result in the propagation of combustion wave with velocity up to 1000m/s and can be a plausible explanation of the origin of dust explosion in coal mines.Comment: 45 pages, 14 figures. Accepted for publication Combustion and Flame 29 June 201

Ignition of thermally sensitive explosives between a contact surface and a shock

The dynamics of ignition between a contact surface and a shock wave is investigated using a one-step reaction model with Arrhenius kinetics. Both large activation energy asymptotics and high-resolution finite activation energy numerical simulations are employed. Emphasis is on comparing and contrasting the solutions with those of the ignition process between a piston and a shock, considered previously. The large activation energy asymptotic solutions are found to be qualitatively different from the piston driven shock case, in that thermal runaway first occurs ahead of the contact surface, and both forward and backward moving reaction waves emerge. These waves take the form of quasi-steady weak detonations that may later transition into strong detonation waves. For the finite activation energies considered in the numerical simulations, the results are qualitatively different to the asymptotic predictions in that no backward weak detonation wave forms, and there is only a weak dependence of the evolutionary events on the acoustic impedance of the contact surface. The above conclusions are relevant to gas phase equation of state models. However, when a large polytropic index more representative of condensed phase explosives is used, the large activation energy asymptotic and finite activation energy numerical results are found to be in quantitative agreement

Morphological characterization of shocked porous material

Morphological measures are introduced to probe the complex procedure of shock wave reaction on porous material. They characterize the geometry and topology of the pixelized map of a state variable like the temperature. Relevance of them to thermodynamical properties of material is revealed and various experimental conditions are simulated. Numerical results indicate that, the shock wave reaction results in a complicated sequence of compressions and rarefactions in porous material. The increasing rate of the total fractional white area $A$ roughly gives the velocity $D$ of a compressive-wave-series. When a velocity $D$ is mentioned, the corresponding threshold contour-level of the state variable, like the temperature, should also be stated. When the threshold contour-level increases, $D$ becomes smaller. The area $A$ increases parabolically with time $t$ during the initial period. The $A(t)$ curve goes back to be linear in the following three cases: (i) when the porosity $\delta$ approaches 1, (ii) when the initial shock becomes stronger, (iii) when the contour-level approaches the minimum value of the state variable. The area with high-temperature may continue to increase even after the early compressive-waves have arrived at the downstream free surface and some rarefactive-waves have come back into the target body. In the case of energetic material ... (see the full text)Comment: 3 figures in JPG forma