21,935 research outputs found
On the One-dimensional Stability of Viscous Strong Detonation Waves
Building on Evans function techniques developed to study the stability of
viscous shocks, we examine the stability of viscous strong detonation wave
solutions of the reacting Navier-Stokes equations. The primary result,
following the work of Alexander, Gardner & Jones and Gardner & Zumbrun, is the
calculation of a stability index whose sign determines a necessary condition
for spectral stability. We show that for an ideal gas this index can be
evaluated in the ZND limit of vanishing dissipative effects. Moreover, when the
heat of reaction is sufficiently small, we prove that strong detonations are
spectrally stable provided the underlying shock is stable. Finally, for
completeness, the stability index calculations for the nonreacting
Navier-Stokes equations are includedComment: 66 pages, 7 figure
Theory of weakly nonlinear self sustained detonations
We propose a theory of weakly nonlinear multi-dimensional self sustained
detonations based on asymptotic analysis of the reactive compressible
Navier-Stokes equations. We show that these equations can be reduced to a model
consisting of a forced, unsteady, small disturbance, transonic equation and a
rate equation for the heat release. In one spatial dimension, the model
simplifies to a forced Burgers equation. Through analysis, numerical
calculations and comparison with the reactive Euler equations, the model is
demonstrated to capture such essential dynamical characteristics of detonations
as the steady-state structure, the linear stability spectrum, the
period-doubling sequence of bifurcations and chaos in one-dimensional
detonations and cellular structures in multi- dimensional detonations
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
Pointwise Green function bounds and stability of combustion waves
Generalizing similar results for viscous shock and relaxation waves, we
establish sharp pointwise Green function bounds and linearized and nonlinear
stability for traveling wave solutions of an abstract viscous combustion model
including both Majda's model and the full reacting compressible Navier--Stokes
equations with artificial viscosity with general multi-species reaction and
reaction-dependent equation of state, % under the necessary conditions of
strong spectral stability, i.e., stable point spectrum of the linearized
operator about the wave, transversality of the profile as a connection in the
traveling-wave ODE, and hyperbolic stability of the associated Chapman--Jouguet
(square-wave) approximation. Notably, our results apply to combustion waves of
any type: weak or strong, detonations or deflagrations, reducing the study of
stability to verification of a readily numerically checkable Evans function
condition. Together with spectral results of Lyng and Zumbrun, this gives
immediately stability of small-amplitude strong detonations in the small
heat-release (i.e., fluid-dynamical) limit, simplifying and greatly extending
previous results obtained by energy methods by Liu--Ying and Tesei--Tan for
Majda's model and the reactive Navier--Stokes equations, respectively
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