455 research outputs found
Dynamics of Hydrogen-Oxygen-Argon Cellular Detonations with a Constant Mean Mass Divergence
The present work revisits the problem of modelling the real gaseous
detonation dynamics at the macro-scale by simple steady one-dimensional (1D)
models. Experiments of detonations propagating in channels with exponentially
expanding cross-sections (exponential horns) were conducted in the H2/O2/Ar
reactive system. Steady detonation waves were obtained at the macro-scale, with
cellular structures characterized by reactive transverse waves. For all the
mixtures studied, the dependence of the mean detonation speed was found to be
in excellent agreement with first principles predictions of quasi-1D detonation
dynamics with lateral mass divergence predicted from detailed chemical kinetic
models. This excellent agreement departs from the earlier experiments of
Radulescu and Borzou (2018) in more unstable detonations. The excellent
agreement is likely due to the much longer reaction zone lengths of diluted
hydrogen oxygen detonations at low pressures, as compared with the
characteristic induction zone lengths. While the cellular instability modifies
the detonation structure induction zone, the detonation dynamics at the
macro-scale are arguably controlled by its hydrodynamic thickness. Near the
limit, minor discrepancy is observed, with the experimental detonations
typically continuing to propagate to slightly higher lateral strain rates and
higher velocity deficits
Dynamics of shock induced ignition in Fickett's model with chain-branching kinetics: influence of
The problem of shock induced ignition by a piston is addressed in the
framework of Fickett's model for reactive compressible flows, i.e., the
reactive form of Burgers' equation. An induction-reaction two-step
chain-branching model is used to study the coupling between the energy release
and the compressible hydrodynamics occurring during the shock ignition
transient leading to a detonation. Owing to the model's simplicity, the
ignition and acceleration mechanism is explained using the two families of
characteristics admitted by the model. The energy release along the particle
paths provides the amplification of forward-travelling pressure waves. These
waves pre-compress the medium in the induction layer ahead of the reaction
zone, therefore changing the induction delays of successive particles. The
variation of the induction delay provides the modulation of the amplification
of the forward travelling pressure waves by controlling the residence time of
the pressure waves in the reaction zone. A closed form analytical solution is
obtained by the method of characteristics and high activation energy
asymptotics. The acceleration of the reaction zone was found to be proportional
to the product of the activation energy, the ratio of the induction to reaction
time and the heat release. This finding provides a theoretical justification
for the previous use of this non-dimensional number to characterize the
ignition regimes observed experimentally in detonations and shock induced
ignition phenomena. Numerical simulations are presented and analysed. Both
subsonic and supersonic internal flame propagation regimes are observed,
consistent with experiment and previous reactive Euler models.Comment: submitted to Proceedings of the Combustion Institut
Shock instability in dissipative gases
Previous experiments have revealed that shock waves in thermally relaxing
gases, such as ionizing, dissociating and vibrationally excited gases, can
become unstable. To date, the mechanism controlling this instability has not
been resolved. Previous accounts of the D'yakov-Kontorovich instability, and
Bethe-Zel'dovich-Thompson behaviour could not predict the experimentally
observed instability. To address the mechanism controlling the instability, we
study the propagation of shock waves in a simple two-dimensional dissipative
hard disk molecular model. To account for the energy relaxation from
translational degrees of freedom to higher modes within the shock wave
structure, we allow inelastic collisions above an activation threshold. When
the medium allows finite dissipation, we find that the shock waves are unstable
and form distinctive high density non-uniformities and convective rolls on
their surface. Using analytical and numerical results for the shock Hugoniot,
we show that both DK and BZT instabilities can be ruled out. Instead, the
results suggest that the clustering instability of Goldhirsch and Zanetti in
dissipative gases is the dominant mechanism
Evolution and stability of shock waves in dissipative gases characterized by activated inelastic collisions
Previous experiments have revealed that shock waves driven through
dissipative gases may become unstable, for example, in granular gases, and in
molecular gases undergoing strong relaxation effects. The mechanisms
controlling these instabilities are not well understood. We successfully
isolated and investigated this instability in the canonical problem of piston
driven shock waves propagating into a medium characterized by inelastic
collision processes. We treat the standard model of granular gases, where
particle collisions are taken as inelastic with constant coefficient of
restitution. The inelasticity is activated for sufficiently strong collisions.
Molecular dynamic simulations were performed for 30,000 particles. We find that
all shock waves investigated become unstable, with density non-uniformities
forming in the relaxation region. The wavelength of these fingers is found
comparable to the characteristic relaxation thickness. Shock Hugoniot curves
for both elastic and inelastic collisions were obtained analytically and
numerically. Analysis of these curves indicate that the instability is not of
the Bethe-Zeldovich-Thompson or Dyakov-Kontorovich types. Analysis of the shock
relaxation rates and rates for clustering in a convected fluid element with the
same thermodynamic history outruled the clustering instability of a homogeneous
granular gas. Instead, wave reconstruction of the early transient evolution
indicates that the onset of instability occurs during the re-pressurization of
the gas following the initial relaxation of the medium behind the lead shock.
This re-pressurization gives rise to internal pressure waves in the presence of
strong density gradients. This indicates that the mechanism of instability is
more likely of the vorticity-generating Richtmyer-Meshkov type, relying on the
action of the inner pressure waves development during the transient relaxation
A nonlinear evolution equation for pulsating detonations using Fickett's model with chain branching kinetics
The detonation wave stability is addressed using Fickett's equation, i.e.,
the reactive form of Burgers' equation. This serves as a simple analogue to the
reactive Euler equations, permitting one to gain insight into the nonlinear
dynamics of detonation waves. Chemical kinetics were modeled using a two-step
reaction with distinct induction and reaction zones. An evolution equation for
the detonation structure was derived using the method of matched asymptotics
for large activation energy and slow rate of energy release. While the first
order solution was found unconditionally unstable, the second order evolution
equation predicted both stable and unstable solutions. The neutral stability
boundary was found analytically, given by , where is the product
of activation energy and the ratio of induction to reaction time. This
reproduces accurately what has been previously established for the reactive
Euler equations and verified experimentally. The evolution equation also
captures stable limit cycle oscillations in the unstable regime and offers
unique insight into the instability mechanism. The mechanism amplifying the
perturbations lies within the induction zone, where the Arrhenius-type rate
equation provides a large change in induction times for small perturbations.
The mechanism attenuating the perturbations arises from acoustic effects, which
delays the amplification of the shock front. The longer the detonation wave,
the more time it takes for the amplification from the reaction zone to reach
the shock front, creating gradients that counter-act the amplification from the
flame acceleration. The results agree with direct numerical simulation, as well
as recovering many similarities with the reactive Euler equation.Comment: Preprint submitted to proceedings of the 15th ID
Non-equilibrium effects on thermal ignition using hard sphere molecular dynamics simulations
The present study addresses the role of molecular non-equilibrium effects in
thermal ignition problems. We consider a single binary reaction of the form A+B
-> C+C. Molecular dynamics calculations were performed for activation energies
ranging between RT and 7.5RT and heat release of 2.5RT and 10RT. The evolution
of up to 10,000 particles was calculated as the system undergoes a thermal
ignition at constant volume. Ensemble averages of 100 calculations for each
parameter set permitted to determine the ignition delay, along with a measure
of the stochasticity of the process. A well behaved convergence to large system
sizes is also demonstrated. The ignition delay calculations were compared with
those obtained at the continuum level using rates derived from kinetic theory:
the standard rate assuming that the distribution of the speed of the particles
is the Maxwell-Boltzmann distribution, and the perturbed rates by Prigogine and
Xhrouet [1] for an isothermal system, and Prigogine and Mahieu [2] for an
energy releasing reaction, obtained by the Chapman-Enskog perturbation
procedure. The molecular results were found in very good agreement with the
latter at low temperatures, confirming that non-equilibrium effects promote the
formation of energetic particles, that serve as seeds for subsequent reaction
events: i.e., hot spots. This effect was found to lower the ignition delay by
up to 30%. At high temperatures, the ignition delay obtained from the standard
equilibrium rate was found to be up to 60% longer than the molecular
calculations. This effect is due to the rapidity of the reactive collisions
that do not allow the system to equilibrate. For this regime, none of the
perturbation solutions obtained by the Chapman-Enskog procedure were valid.
This study thus shows the importance of non-equilibrium effects in thermal
ignition problems, for most temperatures of practical interest.Comment: 18 pages, 11 figure
Viscous solution of the triple shock reflection problem
The reflection of a triple-shock configuration was studied numerically in two
dimensions using the Navier-Stokes equations. The flow field was initialized
using three shock theory, and the reflection of the triple point on a plane of
symmetry was studied. The conditions simulated a stoichiometric methane-oxygen
detonation cell at low pressure on time scales preceding ignition, when the gas
was assumed to be inert. Viscosity was found to play an important role on some
shock reflection mechanisms believed to accelerate reaction rates in
detonations when time scales are small. A small wall jet was present in the
double Mach reflection and increased in size with Reynolds number, eventually
forming a small vortex. Kelvin-Helmholtz instabilities were absent and there
was no Mach stem bifurcation at Reynolds numbers corresponding to when the Mach
stem had travelled distances on the scale of the induction length.
Kelvin-Helmholtz instabilities are found to not likely be a source of rapid
reactions in detonations at time scales commensurate with the ignition delay
behind the Mach stem
Non-uniqueness of solutions in asymptotically self-similar shock reflections
The present study addresses the self-similar problem of unsteady shock
reflection on an inclined wedge. The start-up conditions are studied by
modifying the wedge corner and allowing for a finite radius of curvature. It is
found that the type of shock reflection observed far from the corner, namely
regular or Mach reflection, depends intimately on the start-up condition, as
the flow "remembers" how it was started. Substantial differences were found.
For example, the type of shock reflection for an incident shock Mach number
and an isentropic exponent changes from regular to Mach
reflection between and when a straight wedge tip is used,
while the transition for an initially curved wedge occurs between
and
Multiplicity of detonation regimes in systems with a multi-peaked thermicity
The study investigates detonations with multiple quasi-steady velocities that
have been observed in the past in systems with multi-peaked thermicity, using
Fickett's detonation analogue. A steady state analysis of the travelling wave
predicts multiple states, however, all but the one with the highest velocity
develop a singularity after the sonic point. Simulations show singularities are
associated with a shock wave which overtakes all sonic points, establishing a
detonation travelling at the highest of the predicted velocities.
Under a certain parameter range, the steady-state detonation can have
multiple sonic points and solutions. Embedded shocks can exist behind sonic
points, where they link the weak and strong solutions. Sonic points whose
characteristics do not diverge are found to be unstable, and to be the source
of the embedded shocks. Numerical simulations show that these shocks are only
quasi-stable. This is believed to be due in part to a feature of the model
which permits shocks anywhere behind a sonic point
Chapman-Jouguet deflagrations and their transition to detonation
We study experimentally fast flames and their transition to detonation in
mixtures of methane, ethane, ethylene, acetylene, and propane mixtures with
oxygen. Following the interaction of a detonation wave with a column of
cylinders of varying blockage ratio, the experiments demonstrate that the fast
flames established are Chapman-Jouguet deflagrations, in excellent agreement
with the self-similar model of Radulescu et al. (2015). The experiments
indicate that these Chapman-Jouguet deflagrations dynamically restructure and
amplify into fewer stronger modes until the eventual transition to detonation.
The transition length to a self-sustained detonation was found to correlate
very well with the mixtures' sensitivity to temperature fluctuations, reflected
by the parameter introduced by Radulescu, which is the product of the
non-dimensional activation energy and the ratio of chemical induction
to reaction time . Correlation of the measured DDT lengths determined
that the relevant characteristic time scale from chemical kinetics controlling
DDT is the energy release or excitation time . Correlations with the cell
size also capture the dependence of the DDT length on for fixed blockage
ratios.Comment: 11 figures and 4 videos, manuscript submitted to the Proceedings of
the Combustion Institute to be presented at the the International Combustion
Symposium in Seoul, 201
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