Arkady Petchenko

Flame propagation along the vortex axis

The problem of how to include fast burning along the vortex axis into the general description of turbulent flames is discussed. It is shown that, from such a point of view, the most representative geometry of the flow is burning in a hypothetic ‘tube’ with rotating gaseous mixture. Direct numerical simulations of flame propagation in the hypothetic tube are performed on the basis of the complete system of hydrodynamic equations, including thermal conduction, diffusion, viscosity and chemical kinetics written in the rotational reference frame. The geometry of an axisymmetric flame front is studied, which allows reducing the dimension of the problem by one, thus saving computational time. The numerical results are analysed using the ideas of bubble rising in the acceleration field created by the centrifugal force. It is shown that the velocity of flame propagation is determined mostly by the velocity of bubble rising when the frequency of the tube rotation is sufficiently large. When the rotational frequency is moderate, then the velocity of flame propagation is determined by the planar flame velocity, by the hydrodynamic flame instability and by the gas rotation. Calculations given in the present paper are in agreement with the previous theoretical and experimental results.

ON THE THEORY OF TURBULENT FLAME VELOCITY

The renormalization ideas of self-similar dynamics of a strongly turbulent flame front are applied to the case of a flame with realistically large thermal expansion of the burning matter. In that case a flame front is corrugated both by external turbulence and the intrinsic flame instability. The analytical formulas for the velocity of flame propagation are obtained. It is demonstrated that the flame instability is of principal importance when the integral turbulent length scale is much larger than the cutoff wavelength of the instability. The developed theory is used to analyze recent experiments on turbulent flames propagating in tubes.

INCREASE OF THE FLAME VELOCITY IN A ROTATING GAS AND THE RENORMALIZATION APPROACH TO TURBULENT BURNING

Abstract Propagation of a premixed flame in a rotating gas (along the vortex axis) is considered for the cases of both small and realistically large density drop at the flame front. A nonlinear equation for the flame front is derived, which takes into account the centrifugal force of the vortex, the intrinsic Darrieus–Landau instability of the flame front and the finite flame thickness. Influence of the gas rotation on the flame velocity is investigated numerically as a solution to an eigenvalue problem on the basis of the derived equation. In the domain of weak turbulence such a method provides much better accuracy than direct numerical simulations performed earlier for a similar problem. The solution obtained supplies important information for the renormalization theory of turbulent flame velocity. It is found that turbulent vortices parallel to the direction of flame propagation are more important than the perpendicular ones, which were considered traditionally as the main reason for flame wrinkling. As an illustration, velocity of a strongly turbulent flame is calculated and compared to the experimental results.