Acoustic Perturbation Equations for Reacting Flows to Compute Combustion Noise

Acoustic perturbation equations for reacting flows (APE-RF) are derived to investigate combustion noise in conjunction with a hybrid approach. The method uses large-eddy simulation (LES) data in the first step and the APE-RF system in the second step. The newly derived APE-RF system contains several source terms on the right-hand side (RHS). They are discussed in detail with respect to their relation to various sound mechanisms. The acoustic sources contain the impact of unsteady heat release, non-isomolar combustion, species diffusion, heat diffusion, viscous effects, non-uniform mean flow and non-constant combustion pressure effects, and the influence of acceleration of density inhomogeneities. It is shown that the unsteady heat release occurs in the total time derivative of the density that is immediately available from an LES. By computing via the hybrid method the sound field of an open turbulent non-premixed flame being generated just by the substantial derivative of the density, which contains besides the unsteady heat release, the effect of non-isomolar combustion, heat and species diffusion, and viscous effects, i.e., the remaining terms are neglected, and by comparing the numerical data with experimental findings the total temporal derivative of the density is shown to contain for a wide frequency range the major sound sources in reacting flows. However, it is also indicated that to simulate all the details in the complete frequency range the remaining source mechanisms occurring on the RHS of the APE-RF system are to be taken into account in the analysis.