A numerical model for temperature gradient and particle effects on Rijke burner oscillations

Equations that describe acoustic oscillations in a Rijke burner have been developed. Eigenvalues giving frequencies and growth rates of acoustic modes can be calculated from these equations. In their most general form, these acoustic equations include the effects of nonuniform gas temperature and entrained, burning particles. In general, analytical solution of the equations is not possible. A computer program has been developed that uses numerical methods to calculate eigenvalues from the general equations. For some limiting cases, analytical solution of the equations is possible. Analytical solutions are presented for three such cases. Eigenvalues predicted by the numerical model compare well to the analytical solutions. The Bailey and McIntosh flame-acoustic interaction models were tested with the computer program. Predicted frequencies and growth rates agreed well with experimental data when heat loss was taken into account. The program matched one experimental frequency and growth rate exactly when a time lag was added to the Bailey model. The McIntosh model did nearly as well without any adjustments. A particle combustion-acoustic interaction model for burning aluminum particles has been developed. This model was also tested in the Rijke burner model. The predictions show qualitative but not quantitative agreement with experimental measurements of particle combustion effects. A mechanism is suggested that may explain the discrepancy.