Numerical analysis of the acoustic field of reacting flows via acoustic perturbation equations

The acoustic radiation of a turbulent non-premixed flame using a hybrid method is numerically simulated. The two-step method consists of an incompressible large-eddy simulation (LES) and acoustic perturbation equations (APE), which are reformulated to account for reacting flow effects (APE-RF). In reacting flows, hybrid methods to compute acoustic radiation have some advantages compared to the direct simulation of the acoustic field using a compressible LES. Considering the different characteristic length scales optimized schemes can be applied to each subproblem, i.e., to the hydrodynamic and the acoustic problem. This is of interest since the fluid mechanics is governed by the combustion process and to compute the highly intricate chemistry tailor-made schemes with reasonable computational costs combustion models can be implemented to resolve this phenomenon by, for instance, preprocessed databases for the chemical reactions, like in the steady flamelet approach.The APE-RF system possesses several source terms on the right-hand side (RHS), which are thoroughly discussed to their relation to various sound mechanisms. The acoustic sources describe 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. Moreover, an additional source term within the APE-RF pressure–density relation can be identified to describe the local acoustic wave amplification due to acoustic–flame interaction. It is evidenced that the well-known Rayleigh criterion can be directly given by this source.The unsteady heat release is shown to occur in the total time derivative of the density that is directly provided from an LES solution. By analyzing via the two-step method the acoustic field of an open turbulent non-premixed flame being generated just by the total temporal derivative of the density, and by comparing the numerical data with experimental findings the total substantial derivative is shown to describe for a wide frequency range the essential sound propagation caused by reacting flows. Nevertheless, it is also discussed that to simulate all the details over the complete frequency range additional source mechanisms occurring on the RHS of the APE-RF system are to be considered in the investigation.