Asymptotic methods in turbulent combustion

Abstract

Introduction T are a number of different regimes of turbulent combustion, dependent upon the intensity and scales of the turbulence, measured with respect to suitable combustion parameters derived from the chemical reaction rates. In one set of these regimes, combustion occurs in thin reaction sheets, transported and distorted by the turbulence. In these reaction sheet regimes, more than one characteristic length scale is involved in the turbulent combustion; there are short scales associated with the chemical processes and long scales associated with the turbulence. The disparity of scales causes asymptotic methods to be advantageous for studying turbulent combustion in reaction sheet regimes. A significant amount of progress has been made recently by use of asymptotic methods for describing these regimes in both premixed and nonpremixed turbulent combustion. By and large, the objectives have been not to calculate the turbulent reacting flows completely, but rather to relate the properties of interest in these flows to properties of nonreacting turbulent flows. It then becomes possible to use the existing methods of analysis of nonreacting flows to calculate the results of interest for turbulent combustion. The intent of the present paper is to review the recent advances achieved by use of the methods described above and to identify not only what is known but also areas of unknowns for future research. Other reviews covering material of this type have been published.' The techniques employed in analyzing turbulent combustion differ for premixed and nonpremixed systems. This is especially true in various finer details of analyses of reaction sheet regimes. Therefore, it will be convenient here to treat turbulent premixed flames and turbulent diffusion flames separately. Presentations more unified in character may become appropriate in the future since there are a number of similarities, e.g., the reaction sheet aspect itself. However, it seems likely that certain essential differences will remain; burning velocities exist for premixed but not for nonpremixed combustion (at least not in the same sense).