The evolution of free turbulent spherical gas flames and the generalized Kolmogorov-Obukhov laws

Abstract

A scenario of self-turbulization and limiting (experimentally observed) laws of accelerated expansion of a free turbulent spherical flame in a preliminarily mixed fuel gas mixture are described. The limiting self-similar law of the growth of a completely turbulized spherical front R ∼ 〈ɛ〉1/2t3/2 was shown to correspond to the generalized Kolmogorov-Obukhov law for a locally isotropic velocity field in a spherical turbulent medium with an immobile center of gravity at a constant rate of internal heat release per 1 kg of the mixture 〈ɛ〉 (in m2/s3). The asymptotic dependences of the kinematic (space-time) characteristics of the evolution of a turbulent macroelement growing according to the Kolmogorov-Obukhov laws on the Reynolds and Peclet numbers obtained from the visible radius R, the rate of its propagation R′, and laminar viscosity (v) and thermal diffusivity (χ) coefficients of the initial mixture were obtained in the criterional form. It was shown that, irrespective of the direction of cloud growth under study (horizontal impurity diffusion in the atmosphere and ocean or an isotropic spherical flame) and the physical nature and value of internal heat release 〈ɛ〉 in this direction (viscous dissipation of the kinetic energy of turbulent vortices in the first case or energy release in combustion in the second), the kinematic parameters of the growth of turbulent macroformations were described by these generalized laws.