41 research outputs found
The Darrieus-Landau instability in fast deflagration and laser ablation
The problem of the Darrieus-Landau instability at a discontinuous
deflagration front in a compressible flow is solved. Numerous previous attempts
to solve this problem suffered from the deficit of boundary conditions. Here,
the required additional boundary condition is derived rigorously taking into
account the internal structure of the front. The derived condition implies a
constant mass flux at the front; it reduces to the classical Darrieus-Landau
condition in the limit of an incompressible flow. It is demonstrated that in
general the solution to the problem depends on the type of energy source
present in the system. In the common case of a strongly localized source,
compression effects make the Darrieus-Landau instability considerably weaker.
In particular, the Darrieus-Landau instability growth rate is reduced for laser
ablation in comparison with the classical incompressible case. The instability
disappears completely in the Chapman-Jouguet regime of ultimately fast
deflagration.Comment: 24 pages, 3 figures, version to appear in Physics of Plasma
Influence of gas compression on flame acceleration in the early stage of burning in tubes
The mechanism of finger flame acceleration at the early stage of burning in
tubes was studied experimentally by Clanet and Searby [Combust. Flame 105: 225
(1996)] for slow propane-air flames, and elucidated analytically and
computationally by Bychkov et al. [Combust. Flame 150: 263 (2007)] in the limit
of incompressible flow. We have now analytically, experimentally and
computationally studied the finger flame acceleration for fast burning flames,
when the gas compressibility assumes an important role. Specifically, we have
first developed a theory through small Mach number expansion up to the
first-order terms, demonstrating that gas compression reduces the acceleration
rate and the maximum flame tip velocity, and thereby moderates the finger flame
acceleration noticeably. This is an important quantitative correction to
previous theoretical analysis. We have also conducted experiments for
hydrogen-oxygen mixtures with considerable initial values of the Mach number,
showing finger flame acceleration with the acceleration rate much smaller than
those obtained previously for hydrocarbon flames. Furthermore, we have
performed numerical simulations for a wide range of initial laminar flame
velocities, with the results substantiating the experiments. It is shown that
the theory is in good quantitative agreement with numerical simulations for
small gas compression (small initial flame velocities). Similar to previous
works, the numerical simulation shows that finger flame acceleration is
followed by the formation of the "tulip" flame, which indicates termination of
the early acceleration process.Comment: 19 pages, 20 figure
Low vorticity and small gas expansion in premixed flames
Different approaches to the nonlinear dynamics of premixed flames exist in
the literature: equations based on developments in a gas ex- pansion parameter,
weak nonlinearity approximation, potential model equation in a coordinate-free
form. However the relation between these different equations is often unclear.
Starting here with the low vor- ticity approximation proposed recently by one
of the authors, we are able to recover from this formulation the dynamical
equations usually obtained at the lowest orders in gas expansion for plane on
average flames, as well as obtain a new second order coordinate-free equation
extending the potential flow model known as the Frankel equation. It is also
common to modify gas expansion theories into phenomelogical equations, which
agree quantitatively better with numerical simula- tions. We discuss here what
are the restrictions imposed by the gas expansion development results on this
process
The Rayleigh-Taylor instability and internal waves in quantum plasmas
Influence of quantum effects on the internal waves and the Rayleigh-Taylor
instability in plasma is investigated. It is shown that quantum pressure always
stabilizes the RT instability. The problem is solved both in the limit of
short-wavelength perturbations and exactly for density profiles with layers of
exponential stratification. In the case of stable stratification, quantum
pressure modifies the dispersion relation of the inertial waves. Because of the
quantum effects, the internal waves may propagate in the transverse direction,
which was impossible in the classical case. A specific form of pure quantum
internal waves is obtained, which do not require any external gravitational
field.Comment: 9 pages, 2 figure
The structure of weak shocks in quantum plasmas
The structure of a weak shock in a quantum plasma is studied, taking into
account both dissipation terms due to thermal conduction and dispersive quantum
terms due to the Bohm potential. Unlike quantum systems without dissipations,
even a small thermal conduction may lead to a stationary shock structure. In
the limit of zero quantum effects, the monotonic Burgers solution for the weak
shock is recovered. Still, even small quantum terms make the structure
non-monotonic with the shock driving a train of oscillations into the initial
plasma. The oscillations propagate together with the shock. The oscillations
become stronger as the role of Bohm potential increases in comparison with
thermal conduction. The results could be of importance for laser-plasma
interactions, such as inertial confinement fusion plasmas, and in astrophysical
environments, as well as in condensed matter systems.Comment: 13 pages, 4 figures, version to appear in Physics of Plasma