Numerical modeling of axisymmetric laminar diffusion flames

Recent advances in the development of computational algorithms, reaction kinetics, and mainframe supercomputers have enabled the combustion scientist to investigate chemically reacting systems that were computationally infeasible only a few years ago. In particular, the coupling of adaptive numerical methods with large memory parallel/vector computers has produced an extremely powerful tool with which to probe flame structure. The difficulties in solving high heat release combustion problems, such as flames, center on the large number of equations that must be solved for the elementary chemical species, the exponential nonlinearities that occur in the governing partial differential equations, and the disparate length scales that must be resolved in the computed solution. In this paper we investigate numerically one such reacting system-the axisymmetric laminar diffusion flame. Such flames are important in the interaction of heat and mass transfer with chemical reactions in gas turbines and commercial burners. The ability to predict the coupled effects of complex transport phenomena with detailed chemical kinetics in these flames is critical in modeling turbulent reacting flows, in improving engine efficiency, and in understanding the processes by which pollutants are formed. In our study we consider an unconfined configuration in which a cylindrical fuel stream is surrounded by a coflowing oxidizer jet. Computationally, we solve the governing conservation equations of mass, momentum, species balance, and energy with detailed transport and finite rate chemistry submodels. A discrete solution is obtained on a two-dimensional grid by employing Newton's method with adaptive mesh refinement. Unlike some models in which diffusion in the axial direction is neglected, we consider the fully elliptic problem. The computations are performed in parallel using up to six processors of an IBM ES/3090 600J. The study undertaken in this paper represents the first time that hydrocarbon chemistry with two carbon atoms has been modeled in an elliptic formulation of a laminar flame. The results of this investigation can enable the combustion scientist to probe the fluid dynamics-thermochemistry interaction and its effect on the structure of coflowing methane-air diffusion flames. The study also illustrates the applicability of partial equilibrium/full equilibrium chemistry approximations in diffusion flames and provides an assessment of the use of mole fraction versus mixture fraction correlations for flamelet models of turbulent combustion.