Numerical analysis of the acoustics of a diffusion flame

The aim of this work is to obtain an analytical–numerical solution for a jet diffusion flame in a closed domain and analyze its acoustic field. The combustion chamber is a closed three-dimensional region in which a jet of methane is injected separated from the jet of air. To analyze the influence of the flame under the acoustic field, two tests are performed: in the first test occurs only the mixing, and in the second test occurs the mixing and the chemical reactions. The proposed model uses the Navier–Stokes, mass conservation and wave equations, which are solved numerically. The flow equations are coupled with the equations for the mass fraction of chemical species and temperature, which are solved analytically based on the flamelet model. The numerical scheme follows the finite difference method and the Runge–Kutta multistage scheme is employed for the integration in time. An estimate for the error is presented based on the solution of three grids using the error estimator of Richardson. The results show good agreement with data from the literature. The proposed model is a quick and less expensive option to investigate the acoustic field of reactive flows in a closed region.