Transfer functions of acoustic, entropy and vorticity waves in an annular model combustor and nozzle for the prediction of the ratio between indirect and direct combustion noise

In the present study an annular model combustor and a convergent-divergent nozzle are investigated under realistic operating conditions to examine the basic effects of both direct and indirect combustion noise generation. For that purpose a hybrid CFD/ CAA approach (Computational Fluid Dynamics/ Computational Aero-Acoustics) is applied, which comprises frequency domain simulations of linear fluctuations around a stationary mean flow field. In this study the mean flow is calculated from quasi one-dimensional theory. By this means the coupling behavior between acoustic, entropy and vorticity waves and the fluctuating heat release is computed and evaluated in terms of frequency-dependent transfer functions. The numerical results both for the annular model combustor as well as for the nozzle are validated by recently published analytical models. An excellent agreement between analytical and numerical results is obtained for plane waves propagating in the model combustor. This also applies to higher acoustic transversal waves. The entropy and vorticity transfer functions are well predicted in the low frequency regime, but show however significant deviations to the analytical solution with increasing frequency. Both the acoustic and entropy transfer function of the quasi one-dimensional nozzle are captured by the hybrid approach with high accuracy. Finally the transfer functions of the annular combustor and the nozzle are concatenated to determine the ratio between indirect and direct noise emissions for plane waves. In accordance with previous studies it is found that the impact of the indirect noise on the total noise increases with the mean flow acceleration and in the low frequency regime. The influence of reflections from the combustor outlet on the noise ratio is identified by replacing the nozzle by a reflecting boundary condition. In this case the indirect noise dominates the direct noise at various distinct frequencies.