Analysis of unsteady one-dimensional homogeneous diffusion flames at constant pressure.

Analytical and numerical solutions for unsteady diffusive burning of H$\sb2$/N$\sb2$ fuel strips, cylinders and spheres in air were compared to detailed numerical simulations of H$\sb2$/N$\sb2$ mixtures burning in air with full-chemistry, multi-component diffusion and thermal conductivity. Approximate solutions using constant or variable density with fast chemistry were obtained in order to assess the effects of exothermicity. The rate of fuel consumption of cylindrical and spherical flames increased significantly due to exothermicity, in contrast to planar or strip flames which maintained the same rate of fuel consumption for constant or variable density. The burning times of fuel spheres and cylinders with variable density were significantly smaller than the burning times of fuel spheres and cylinders assuming constant density. The burning times of planar flames were not affected by exothermicity, but the maximum flame expansion was greater than that of cylindrical or spherical flames. The detailed numerical simulations indicated that the mixture fraction profiles are non-monotonic and that the scalar dissipation based on the mixture fraction of H atoms is zero or not well defined at the points of peak temperature during most of the burning time, due to differential diffusion effects. The kinetic parameters of equivalent single step reactions were obtained from the profiles of the rate of heat release in the detailed simulations. The influence of diffusion coefficients on results obtained using single step reaction models was determined. The residual fuel mass, maximum temperature and flame location, as determined from the simplified model calculations, were compared to those from the full chemistry simulations, in order to establish the appropriate choices of diffusion coefficients and reaction parameters in the approximate calculations. A major conclusion is that compromises have to be made in the parameters used in the approximate models to match all these variables simultaneously.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104605/1/9542817.pdfDescription of 9542817.pdf : Restricted to UM users only