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