The spectral theory of turbulent-flame propagation

Abstract

This paper is concerned with turbulent-flame propagation. An analytical formulation for large or small scale, low-intensity turbulent flames is based on the distribution of eddy sizes present in the flow stream. The validity of several turbulent-flame theories is checked as well as the reactionzone-model criterion of Kovasznay, with a modified Powling type burner to produce a low-pressure stream of propane and air with small-scale, low-intensity isotropic turbulence. The basic assumption involved in the analysis is that the large-scale turbulence wrinkles the flame surface, thereby increasing the combustion area, but does not affect the laminar-flame propagation rate. The small-scale turbulence is assumed to alter the laminar-flame propagation by virtue of a change in the transport processes. Both effects are believed to occur simultaneously, producing an increase in the rate of flame propagation. The spectral theory weights the contributions of large and small eddies by considering the distribution of kinetic energy in the velocity fluctuations. The experimental data obtained correspond to the upper limiting condition of the spectral theory, although published data are shown to fall close to a lower limit. In the former case, nearly all the eddies are of smaller or comparable size to that of the reaction zone thickness; whereas, in the latter case, the scale is of larger size. The Kovasznay parameter correlated the experimentally obtained data and correctly described the reaction-zone structure as observed during the testing. The turbulence intensity of ambient air behind a 3/32 inch mesh grid and an x/M position of 50.7 was found to decrease 70 per cent as the pressure varied from 1 to 0.1 atmos. The experimental data of this study were found to be larger in magnitude than that predicted by the Scurlock-Grover Theory but consistent with the experimental results of Grover, et al. This difference may be indicative of the effect of anisotropy on turbulent-flame propagation. The ratio of turbulence microscale to laminar-flame thickness did not appear to be a valid criterion for predicting the reaction-zone structure. Within the limits of the approximations made, the following general conclusions were made. (1) The spectral theory correctly describes turbulent-flame propagation for large- or small-scale, low-intensity flames. (2) The Kovasznay parameter accurately predicts the reaction-zone structure for small-scale, low-intensity turbulent flames. (3) Grid-generated turbulence intensity is dependent on the pressure of the system. (4) The ratio of turbulence microscale to laminar-flame thickness does not constitute a sufficient measure for the prediction of the reaction-zone structure.