Michael A. Liberman

Self-consistent model of the Rayleigh-Taylor instability in ablatively accelerated laser plasma

A self‐consistent approach to the problem of the growth rate of the Rayleigh–Taylor instability in laser accelerated targets is developed. The analytical solution of the problem is obtained by solving the complete system of the hydrodynamical equations which include both thermal conductivity and energy release due to absorption of the laser light. The developed theory provides a rigorous justification for the supplementary boundary condition in the limiting case of the discontinuity model. An analysis of the suppression of the Rayleigh–Taylor instability by the ablation flow is done and it is found that there is a good agreement between the obtained solution and the approximate formula σ = 0.9√gk − 3u1k, where g is the acceleration, u1 is the ablation velocity. This paper discusses different regimes of the ablative stabilization and compares them with previous analytical and numerical works.

Self-acceleration and fractal structure of outward freely propagating flames

Flame acceleration associated with development of the Landau–Darrieus hydrodynamic instability is studied by means of direct numerical simulation of the Navier–Stokes equations including chemical kinetics in the form of the Arrhenius law. The fractal excess for radially expanding flames in cylindrical geometry is evaluated. Two-dimensional (2-D) simulation of radially expanding flames in cylindrical geometry displays a radial growth with 1.25 power law temporal behavior after some transient time. It is shown that the fractal excess for 2-D geometry obtained in the numerical simulation is in good agreement with theoretical predictions. The difference in fractal dimension between 2-D cylidrical and three-dimensional spherical radially expanding flames is outlined. Extrapolation of the obtained results for the case of spherical expanding flames gives a radial growth power law that is consistent with temporal behavior obtained in the survey of experimental data.

Numerical Simulation of Curved Flames in Cylindrical Tubes

Abstract Dynamics of a curved flame front in cylindrical tubes is studied by means of numerical simulation of the complete system of hydrodynamic equations including thermal conduction, fuel diffusion, viscosity and chemical kinetics. The complete three-dimensional system of equations is reduced to a two-dimensional system with the account of cylindrical symmetry of the problem. The dependence of the flame velocity on the tube diameter and the expansion coefficient of the fuel is investigated. It is obtained that the velocity increase due to the curved shape of the flame front is considerably larger for the case of cylindrical tubes compared to the two-dimensional curved flames. The regime of strong initiation of the flame instability is obtained for narrow tubes, when all perturbation modes of small amplitude are stable, but a curved stationary flame is still possible. The simulation results indicate that there is no maximal velocity for curved flames in cylindrical tubes unlike two-dimensional flames. I...

HOT SPOT FORMATION BY THE PROPAGATING FLAME AND THE INFLUENCE OF EGR ON KNOCK OCCURRENCE IN SI ENGINES

Two-dimensional and three-dimensional numerical simulations, which take into account both the low-temperature and high-temperature kinetics and yield correct induction times for hydrocarbon autoignition, are presented. The development of the autoignition is tightly connected to the formation of hot spots that evolved from the nonuniformities caused by pressure waves emitted by the propagating flame. It is shown that there is a considerable feedback: the propagating flame is accelerated by the temperature increase due to development of the cool flames in the end gas, and development of the autoignition is enhanced by the flame acceleration. Knocking onset is the self-ignition of the end-gas, which occurs as a result of combined effects of the end-gas compression by the moving piston during the compression stroke and by the propagating flame together with expanding combustion products. The calculated dependence of the temperature and pressure in the end gas on crank angle and predicted time of the autoignition onset for different engine operation conditions, in particular, for different percentage of EGR are found in a good agreement with the experimental data.

NUMERICAL MODELING OF THE PROPAGATING FLAME AND KNOCK OCCURRENCE IN SPARK-IGNITION ENGINES

ABSTRACT The present paper reports multidimensional numerical simulations of knock occurrence in internal combustion engines. Knock occurrence in spark-ignition engines was examined within the context of a model of autoignition of hydrocarbon/air mixture, which has been extended by including chemical reactions for the propagating flames and an extended chemical model for the cool flames. Special attention was given to the influence of the propagating flame on the autoignition onset. Knocking occurrence is the self-ignition of the end gas as a result of combined effects of the end-gas compression by the moving piston in the compression stroke and by the accelerating propagating flame and expanding combustion products. It is recognized that the autoignition onset is accompanied by an acceleration of the propagating flame that acts as an accelerating piston emanating pressure waves in the end gas. Given the initial fuel/air mixture concentration, temperature, and pressure, the developed model was used to calculate temperature, pressure, species concentration as a function of crank angle, combustion mixture, exhaust gas recycled and engine speed, and the time of the autoignition onset. The model was validated using the experimental data obtained with a Ricardo test engine and excellent agreement was achieved between the modeling predictions and the observed experimental data. In particular it was shown that the increase of the engine speed results in the decrease of the knock onset tendency, allowing the engine to operate with higher compression ratio without knocking.

Experimental Study of the Preheat Zone Formation and Deflagration to Detonation Transition

The authors present experimental studies of the deflagration-to-detonation transition (DDT) in tubes with smooth and rough walls in stoichiometric hydrogen-oxygen and ethylene-oxygen mixtures. On the basis of experimental evidence, it is shown that formation of the preheat zone, where reaction is chemically frozen, promotes the transition to detonation if temperature and width of the preheat zone are above certain critical values. A sequence of high-speed Schlieren records permits an accurate determination of the minimal values of temperature and width of the preheat zone, leading to transition to detonation. The experimentally measured critical temperatures and widths of the preheat zone initiating restructuring of the flame and transition to detonation in hydrogen-oxygen and ethylene-oxygen mixtures are consistent with the developed theory.

Mechanisms of ignition by transient energy deposition : Regimes of combustion wave propagation

Regimes of chemical reaction wave propagating in reactive gaseous mixtures, whose chemistry is governed by chain-branching kinetics, are studied depending on the characteristics of a transient ther ...

Numerical studies of curved stationary flames in wide tubes

The nonlinear problem of the propagation of curved stationary flames in tubes of different widths is studied by means of direct numerical simulation of the complete system of hydrodynamic equations including thermal conduction, viscosity, fuel diffusion and chemical kinetics. While only a planar flame can propagate in a narrow tube of width smaller than half of the cut–off wavelength determined by the linear theory of the hydrodynamic instability of a flame front, in wider tubes stationary curved flames propagate with velocities considerably larger than the corresponding velocity of a planar flame. It is shown that only simple ‘single-hump’ slanted stationary flames are possible in wide tubes, and ‘multi–hump’ flames are possible in wide tubes only as a nonstationary mode of flame propagation. The stability limits of curved stationary flames in wider tubes and the secondary Landau–Darrieus instability are investigated. The dependence of the velocity of the stationary flame on the tube width is studied. The analytical theory describes the flame reasonably well when the tube width does not exceed some critical value. The dynamics of the flame in wider tubes is shown to be governed by a large–scale stability mechanism resulting in a highly slanted flame front. In wide tubes, the skirt of the slanted flame remains smooth with the length of the skirt and the flame velocity increasing progressively with the increase of the tube width above the second critical value. Results of the analytical theory and numerical simulations are discussed and compared with the experimental data for laminar flames in wide tubes.

Nonlinear equation for curved stationary flames

A nonlinear equation describing curved stationary flames with arbitrary gas expansion, θ=ρfuel/ρburnt, subject to the Landau–Darrieus instability, is obtained in a closed form without an assumption of weak nonlinearity. It is proved that in the scope of the asymptotic expansion for θ→1, the new equation gives the true solution to the problem of stationary flame propagation with the accuracy of the sixth order in θ−1. In particular, it reproduces the stationary version of the well-known Sivashinsky equation at the second order corresponding to the approximation of zero vorticity production. At higher orders, the new equation describes influence of the vorticity drift behind the flame front on the flame velocity and the flame front structure. Its asymptotic expansion is carried out explicitly, and the resulting equation is solved analytically at the third order. For arbitrary values of θ, the highly nonlinear regime of fast flow burning is investigated, for which case a large flame velocity expansion of the...

Numerical Study of Curved Flames under Confinement

Dynamics of laminar flames in closed tubes is studied by means of two-dimensional numerical simulations taking into account thermal conduction, fuel diffusion, viscosity and chemical kinetics. Development of the hydrodynamic instability of a flame front is investigated for flames with the chemical reactions of the first and the third order. We found that for a flame with the first order reaction the hydrodynamic instability is strongly reduced or even suppressed in sufficiently short tubes. Unlike this, in the case of a flame of the third order reaction the instability is enhanced due to significant increase of the normal velocity of the planar flame under confinement. The instability development for flames of both the first and the third order reaction is strongly affected by acoustic waves generated by the flame in a closed chamber. Particularly, a weak shock colliding with the flame front may lead to a temporary stabilization of the flame instability. On the contrary, when flame comes to the end of the tube the acoustic waves may cause significant increase of the flame instability. We studied a possibility of the detonation ignition ahead of the flame front as well. We found that the detonation can be ignited at the far end of the tube by the weak shocks and sound waves generated by the flame in a closed tube. Triggering of the detonation ahead of the flame propagating in a closed tube is related to the knock problem in spark-ignition engines.