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

2020 ◽  
Vol 897 ◽  
Author(s):  
Paul Clavin ◽  
Bruno Denet
Keyword(s):  
Heat Release ◽  
Analytical Study ◽  
Gaseous Detonations ◽  
Direct Initiation ◽  
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scholarly journals The role of unsteadiness in direct initiation of gaseous detonations

2000 ◽  
Vol 421 ◽  
pp. 147-183 ◽  
Author(s):  
CHRIS A. ECKETT ◽  
JAMES J. QUIRK ◽  
JOSEPH E. SHEPHERD
Keyword(s):  
Numerical Simulations ◽  
Decay Rate ◽  
Wave Front ◽  
Reaction Zone ◽  
Critical Energy ◽  
Local Analysis ◽  
Zone Structure ◽  
Gaseous Detonations ◽  
Release Wave ◽  
Direct Initiation

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.

Multidimensional stability analysis of gaseous detonations near Chapman–Jouguet conditions for small heat release

2009 ◽  
Vol 624 ◽  
pp. 125-150 ◽  
Author(s):  
PAUL CLAVIN ◽  
FORMAN A. WILLIAMS
Keyword(s):  
Heat Release ◽  
Acoustic Waves ◽  
Realistic Model ◽  
Cellular Structures ◽  
Bifurcation Parameter ◽  
Leading Order ◽  
Instability Mechanism ◽  
Gaseous Detonations ◽  
Detonation Structure ◽  
Rate Of Heat Release

Multidimensional instability of planar detonations, leading to cellular structures, is studied analytically near Chapman–Jouguet conditions, in the limit of small heat release, with small (Newtonian) differences between heat capacities, by using an expansion in a small parameter representing the ratio of the heat release to the thermal enthalpy of the fresh mixture. In this limit, the dynamics of detonations is governed by the interaction between the acoustic waves and the heat-release rate inside the inner detonation structure, the entropy–vorticity wave playing a negligible role at leading order. This situation is just opposite from that considered in our 1997 study of strongly overdriven detonations. The present analysis offers a step towards improving our understanding of the cellular structures of ordinary detonations, for which both the entropy–vorticity waves and the acoustic waves are involved in the instability mechanism. The relevant bifurcation parameter is identified, involving the degree of overdrive and the sensitivity of the rate of heat release to temperature at the Neumann state, and the onset of the instability is studied analytically for a realistic model of the inner structure of gaseous detonations.

On the direct initiation of gaseous detonations by an energy source

1994 ◽  
Vol 277 ◽  
pp. 227-248 ◽  
Author(s):  
Longting He ◽  
Paul Clavin
Keyword(s):  
Energy Source ◽  
Critical Radius ◽  
Critical Value ◽  
Blast Waves ◽  
Initiation Energy ◽  
Point Energy ◽  
Gaseous Detonations ◽  
Curvature Effects ◽  
Direct Initiation ◽  
Steady Solutions

A new criterion for the direct initiation of cylindrical or spherical detonations by a localized energy source is presented. The analysis is based on nonlinear curvature effects on the detonation structure. These effects are first studied in a quasi-steady-state approximation valid for a characteristic timescale of evolution much larger than the reaction timescale. Analytical results for the square-wave model and numerical results for an Arrhenius law of the quasi-steady equations exhibit two branches of solutions with a C-shaped curve and a critical radius below which generalized Chapman–Jouguet (CJ) solutions cannot exist. For a sufficiently large activation energy this critical radius is much larger than the thickness of the planar CJ detonation front (typically 300 times larger at ordinary conditions) which is the only intrinsic lengthscale in the problem. Then, the initiation of gaseous detonations by an ideal point energy source is investigated in cylindrical and spherical geometries for a one-step irreversible reaction. Direct numerical simulations show that the upper branch of quasi-steady solutions acts as an attractor of the unsteady blast waves originating from the energy source. The critical source energy, which is associated with the critical point of the quasi-steady solutions, corresponds approximately to the boundary of the basin of attraction. For initiation energy smaller than the critical value, the detonation initiation fails, the strong detonation which is initially formed decays to a weak shock wave. A successful initiation of the detonation requires a larger energy source. Transient phenomena which are associated with the intrinsic instability of the quasi-steady detonations branch develop in the induction timescale and may induce additional mechanisms close to the critical condition. In conditions of stable or weakly unstable planar detonations, these unsteady phenomena are important only in the vicinity of the critical conditions. The criterion of initiation derived in this paper works to a good approximation and exhibits the huge numerical factor, 106–108, which has been experimentally observed in the critical value of the initiation energy.

scholarly journals Spinning instability of gaseous detonations

2002 ◽  
Vol 466 ◽  
pp. 179-203 ◽  
Author(s):  
ASLAN R. KASIMOV ◽  
D. SCOTT STEWART
Keyword(s):  
Activation Energy ◽  
Heat Release ◽  
Circular Tube ◽  
Hydrodynamic Instability ◽  
Three Dimensional ◽  
Low Frequency ◽  
Initial Pressure ◽  
Neutral Stability ◽  
Arrhenius Model ◽  
Gaseous Detonations

We investigate hydrodynamic instability of a steady planar detonation wave propagating in a circular tube to three-dimensional linear perturbations, using the normal mode approach. Spinning instability is identified and its relevance to the well-known spin detonation is discussed. The neutral stability curves in the plane of heat release and activation energy exhibit bifurcations from low-frequency to high-frequency spinning modes as the heat release is increased at fixed activation energy. With a simple Arrhenius model for the heat release rate, a remarkable qualitative agreement with experiment is obtained with respect to the effects of dilution, initial pressure and tube diameter on the behaviour of spin detonation. The analysis contributes to the explanation of spin detonation which has essentially been absent since the discovery of the phenomenon over seventy years ago.

Internal pressure loads due to gaseous detonations

1993 ◽  
Vol 443 (1918) ◽  
pp. 343-366 ◽  
Keyword(s):  
Strong Shock ◽  
Shock Pressure ◽  
Gaseous Detonation ◽  
Flat Surfaces ◽  
Gaseous Detonations ◽  
Reflected Shock ◽  
Several Variables ◽  
Direct Initiation ◽  
Detonation Transition ◽  
Inert Layer

The internal loading of structures and confinements by gaseous detonation is studied using a multidimensional strong-shock physics code. Hydrogen-air-steam mixtures are used in calculations to show phenomena that apply qualitatively to any detonable gaseous fuel-oxidant-diluent mixture. Several variables are considered with respect to loading: ( a ) inert layers of various thicknesses; ( b ) deflagration-to-detonation transition(DDT) location as compared with direct initiation; and ( c ) some variations in geometry or confinement. Relatively thin inert layers are shown to increase the peak reflected shock pressure over that which would occur if the inert layer were not there. Inert layers may also increase impulse under some circumstances. DDT increases peak reflected pressures over those seen for direct initiation because of precompression of unburned gases. DDT may also increase impulses. Peak reflected pressures and impulses are greater in edges and corners than on flat surfaces. Internal obstruction tends to randomize the energy in a detonation wave, decreasing the impulse on structures, and allowing the pressure to equilibrate more rapidly than if there were no obstruction.

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