Analysis of different sound source formulations to simulate combustion generated noise using a hybrid LES/APE-RF method

Combustion noise and sound source mechanisms of the DLR-A flame are investigated. A hybrid large-eddy simulation/computational aeracoustics (LES/CAA) approach is employed. In the first step of the hybrid analysis the flamelet/progress variable (FPV) model is employed as combustion model followed by the acoustic simulation in the second step using the acoustic perturbation equations for reacting flows (APE-RF). The flamelet/progress variable database has been extended in terms of acoustic source terms. The analysis of the acoustic field of low MACH number reacting flows induced by the thermoacoustic sources such as the unsteady heat release leads to a very stiff problem formulation, since the related sources require highly resolved regions in the source area, which restricts the possible time step. To simulate combustion generated noise using such a hybrid approach, a suitable source description has to be used, which preferably satisfies two requirements, i.e, to efficiently and accurately predict the generated sound field, while the source term can be easily evaluated from the LES. Using the source term, which is expressed via the scaled partial time derivative of the density, the acoustic field can be reproduced best up to a maximum STROUHAL number of St(D) = 2. However, this source formulation requires a rigorous constraint at the interface of the hybrid approach to avoid spurious noise due to artificial acceleration caused by interpolation. To be more precise, the convection speed of density inhomogeneities has to be preserved during interpolation. A compromise between efficiency and accuracy can be achieved using the source formulation expressed via the scaled material derivative of the density, since by definition this formulation does not describe the convection of density inhomogeneities.