Stationary modes of combustion in a fine-scale turbulent stream

Abstract

The majority of models of the turbulent combustion of gases are based mainly on intuitive concepts concerning the processes occurring in the flame. The characteristics of a turbulent flame are estimated from considerations of dimensionality and similarity. A detailed review of works on turbulent combustion is given in [1]. Problems on the calculation of the combustion rate in a turbulent stream as a proper value of the equations of heat and mass transfer and of the corresponding boundary conditions have recently been raised. Here too one must rest on assumptions of a semiempirical nature, which in large measure is connected with the inadequate level of development of turbulence theory. In the present work the equation of propagation of the zone of chemical reactions in the stream is averaged statistically by analogy with studies of turbulent flows. Correct averaging is possible at scales of hydrodynamic disturbances smaller than the flame thickness (fine-scale turbulence). The temperature pulsations are related with the size of the heat flux using the theory of mixing lengths. The main influence is specific to effects arising during averaging of the heat release function. Two stationary modes, distinguished by the normal propagation velocity ω1, are isolated within the framework of the Cauchy problem with a given initial mixture temperature and zero heat flux in the burned gas. A heat conduction mode occurs with a stream velocity ω > ω1 and an induction mode with ω < ω1. An expression is found for ω1 which reflects the principal effects in the flame and which in the limit coincides with the equation of Zel'dovich and Frank-Kamenetskii for a laminar flame. In those cases when the distorting effect of the heat release function is small, the turbulence affects the combustion rate through mechanisms of intensification of transport processes.