Measurement of various terms in the turbulent kinetic energy balance within a flame and comparison with theory

Abstract

Direct measurements have been made of four of the six terms in the exact form of the turbulent kinetic energy (TKE) equation within a premixed turbulent flame, in order to understand how the combustion interacts with the turbulence. Results are compared to the predictions of the Bray-Moss-Libby (B-M-L) model. The mean reaction ( w ) also was estimated from the data, using a local control volume concept. The measurements were made possible by the simultaneous use of laser velocimetry and Rayleigh scattering. Increasing the heat release was found to increase the “flame generated” turbulence as well as the “apparent” turbulence and the turbulent flame speed. Part of this flame-generated turbulence is due to vorticity created by the curved flamelets, as evidenced by the unexpected existence of low speed products. The flame also is found to exert an upstream influence that causes an increase in the turbulence of the pure reactants before these reactants ever reach a flamefront. The measured diffusion term in the TKE balance indicates a countergradient diffusion of TKE toward the center of the flame where TKE is maximum; however, this is not true diffusion since the TKE balance includes apparent turbulence. The B-M-L model correctly predicts quantities which are dominated by intermittency due to flame motion such as the diffusion term in the TKE, and fluxes ϱu″c″ and ϱu″ 2c″ which change sign within the flame. This is because the model successfully accounts for intermittency by separating the physics of reactants and products. The model does not successfully predict even the trends associated with the more subtle “true turbulence” associated with products ( u′ p). It is felt that additional work is needed to remove “apparent turbulence” from the TKE balance, and eventually to replace one closure relation in the model to account for vorticity produced by curved flamelets.