Mathematical Imaging of Piloted Diffusion Methane-Air Flames Under Anisotropic Scalar Dissipation Rates

Abstract

The present work is a numerical simulation of the, piloted, non-premixed, methane–air flame structure in a new mathematical imaging domain. This imaging space has the mixture fraction of diffusion flame Z1 and mixture fraction of pilot flame Z2 as independent coordinates to replace the usual physical space coordinates. The predications are based on the solution of two–dimensional set of transformed second order partial differential conservation equations describing the mass fractions of O2, CH4, CO2, CO, H2O, H2 and sensible enthalpy of the combustion products which are rigorously derived and solved numerically. A three–step chemical kinetic mechanism is adopted. This was deduced in a systematic way from a detailed chemical kinetic mechanism by Peters (1985). The rates for the three reaction steps are related to the rates of the elementary reactions of the full reaction mechanism. The interaction of the pilot flame with the non-premixed flame and the resulting modifications to the structure and chemical kinetics of the flame are studied numerically for different values of the scalar dissipation rate tensor. The dissipation rate tensor represents the flame stretching along Z1, the main mixture fraction, and in the perpendicular direction, along Z2, the pilot mixture fraction. The computed flame temperature contours are plotted in the Z1-Z2 plane for fixed values of the dissipation rate along Z1 and Z2.These temperature contours show that the flame will become unstable when the dissipate rates along Z1 and Z2 increase, simultaneously, to the limiting value for complete flame extinction of 45 s−1. However, the diffusion flame will extinguish for dissipate rates less than 20 1/s, if unpiloted. It is also noticed that the flame will remain stable if the dissipation rate along Z2 is increased to the limiting value, while the dissipation rate, along Z2, remains constant at a value less than 30 s−1.