Vitaliy Bychkov

Nonlinear equation for a curved stationary flame and the flame velocity

A nonlinear equation for a curved stationary flame subject to the Darrieus–Landau instability is obtained for an arbitrary ratio of the fuel density and the density of the burnt matter under the assumptions of a thin flame front and weak nonlinearity. On the basis of the nonlinear equation the velocity of a two-dimensional curved stationary flame is calculated. The obtained velocity is in a good agreement with the results of two-dimensional simulations of flame dynamics in tubes.

Analytical scalings for flame interaction with sound waves

Analytical scalings for the problem of flame interaction with acoustic waves of controlled intensity are obtained on the basis of the linear equation for a perturbed flame front. Both stabilization of the hydrodynamic flame instability by sound waves of small amplitudes and excitation of the parametric instability at the flame front by sound waves of sufficiently large amplitudes are considered. The stability limits obtained analytically agree well with the previous numerical calculations. Besides, the analytical results for the minimum amplitude of sound waves needed to induce the parametric instability and for the typical wavelength of the instability are in excellent agreement with the experimental results on propane flames.

THERMAL-INSTABILITY AND PULSATIONS OF THE FLAME FRONT IN WHITE-DWARFS

It is shown that the thermonuclear flame front in white dwarfs is unstable against one-dimensional thermal instability which leads to the pulsating regime of flame propagation. The efficiency of the instability increases for the flame propagating in the l

Stability of a planar flame front in a compressible flow

The effect of flow compressibility on the hydrodynamic stability of a planar flame front of finite thickness is investigated. It is shown that a flame front becomes more unstable with the increase of the Mach number of the flame generated flow. Particularly, even for a flow with relatively small Mach numbers ∼0.1–0.2 the maximal growth rate of the flame instability becomes 2–3 times larger than the growth rates for a flame in the incompressible flow.

Effect of the Darrieus-Landau instability on turbulent flame velocity.

The propagation of turbulent premixed flames influenced by the intrinsic hydrodynamic flame instability (the Darrieus-Landau instability) is considered in a two-dimensional case using the model nonlinear equation proposed recently by Bychkov [Phys. Rev. Lett. 84, 6122 (2000)]. The nonlinear equation takes into account both the influence of external turbulence and the intrinsic properties of a flame front, such as small but finite flame thickness and realistically large density variations across the flame front. Dependence of the flame velocity on the turbulent length scale, turbulent intensity, and density variations is investigated in the case of weak nonlinearity and weak external turbulence. It is shown that the Darrieus-Landau instability influences the flamelet velocity considerably. The obtained results are in agreement with experimental data on the turbulent burning of moderate values of the Reynolds number.

Effect of temporal pulsations of a turbulent flow on the flame velocity

Recently, a hypothesis has been proposed that temporal pulsations of a turbulent flow may explain the reduction and even saturation of the flame velocity at large turbulent intensities. However, the study was limited to very anisotropic flows. In this paper, we investigate the effect under more general conditions, which use the dependence of the velocity in the mean direction of propagation. Analytical formulae for the flame velocity in a time-dependent turbulent flow are obtained at low turbulent intensity and generalized to high intensity by using the renormalization method. These results are compared to numerical simulations. We show that the temporal pulsations do not lead to saturation of the flame velocity at high turbulent intensity, even if some effects appear at lower root-mean-square velocity.

Influence of compressibility on propagation of curved flames

The nonlinear problem of propagation of a curved stationary flame in a compressible flow is studied by means of two-dimensional numerical simulations of the complete set of equations of flame dynamics including chemical kinetics, thermal conduction, and fuel diffusion. It is shown that curved shape of a flame in a compressible fuel mixture leads to stronger increase of the flame velocity than in the case of isobaric flames. It is found that acceleration of a flame due to the development of the curved shape generates a shock of noticeable intensity ahead of the flame front. The shock compresses the fresh fuel and, in turn, changes parameters of the flame. As a result, strongly curved flames in compressible flows can be observed in tubes much narrower than in the case of isobaric flows. Additional amplification of the flame velocity is obtained due to the development of asymmetrical structures at the flame fronts in wide tubes.

Stabilization of the hydrodynamic flame instability by a weak shock

The problem of stabilization of the hydrodynamic flame instability due to collision of a flame with a weak shock is revised. It is shown that correct treatment of this problem leads to results different from the Markstein solution [G. H. Markstein, Nonsteady Flame Propagation (Pergamon, Oxford, 1964)]. It is obtained that depending on the shock intensity a flame-shock collision may lead to temporary reduction of the perturbation amplitude at the flame front, to complete suppression of initial perturbations, or to inversion of the flame shape. Scalings for the shock intensity leading to stabilization or destabilization of a flame front are obtained.

The nonlinear equation for curved flames applied to the problem of flames in cylindrical tubes

The nonlinear equation for curved stationary flames of realistic expansion coefficients is solved numerically for the problem of flame propagation in cylindrical tubes. Two different configurations of a flame front corresponding to convex and concave flames are obtained. The convex and concave flames propagate with different velocities that depend on the tube radius and on the expansion coefficient of the burning matter. For tubes of a moderate radius the velocity amplification for convex flames exceeds the respective velocity amplification of two-dimensional flames almost twice. For tubes of a large radius unlimited increase of the curved flame velocity with increase of the tube width takes place. The obtained theoretical results are in good quantitative agreement with the results of numerical experiments on flame dynamics in cylindrical tubes.

Flow-flame interaction in a closed chamber

Numerous studies of flame interaction with a single vortex and recent simulations of burning in vortex arrays in open tubes demonstrated the same tendency for the turbulent burning rate proportional to U-rms lambda(2/3), where U-rms is the root-mean-square velocity and lambda is the vortex size. Here, it is demonstrated that this tendency is not universal for turbulent burning. Flame interaction with vortex arrays is investigated for the geometry of a closed burning chamber by using direct numerical simulations of the complete set of gas-dynamic combustion equations. Various initial conditions in the chamber are considered, including gas at rest and several systems of vortices of different intensities and sizes. It is found that the burning rate in a closed chamber (inverse burning time) depends strongly on the vortex intensity; at sufficiently high intensities it increases with U-rms approximately linearly in agreement with the above tendency. On the contrary, dependence of the burning rate on the vortex size is nonmonotonic and qualitatively different from the law lambda(2/3). It is shown that there is an optimal vortex size in a closed chamber, which provides the fastest total burning rate. In the present work, the optimal size is six times smaller than the chamber height.