Nonlinear Response of Diffusion Flames to Uniform Velocity Disturbances

Abstract

This article presents an investigation of the nonlinear response of a diffusion flame to unsteady velocity disturbances. The infinite rate chemistry flame model is employed to study unsteady two-dimensional co-flow non-premixed combustion. In this model, the flame geometry is given by the stoichiometric level surface, which is obtained by the equation for the Schvab-Zeldovich variable. In this article, this equation is solved using an integral equation approach. An approximate analytical expression is obtained for the flame length variation as a function of time. The heat release rate is obtained from thermodynamic calculations. The variation of the heat release rate with the velocity fluctuations is analyzed. It is seen that the flame response to a single frequency of excitation contains several frequencies even though the governing equation is linear. It is shown that the heat release rate has exponential dependence on the amplitude of velocity fluctuations. The nonlinear nature of flame response becomes significant at lower Fourier numbers (for mass transport). A nonlinear model for the transfer function to describe the response of the heat release rate to velocity perturbation has been constructed.

Keywords:

• Diffusion flame
• Nonlinear
• Transfer function
• Unsteady response