The ability to calculate compressible reactive flows enables the computation of thermoacoustic interactions in gas turbine combustor systems. A new projection-based numerical method able to compute compressible reactive flows is developed within this work. This computational scheme is based on a modified Helmholtz decomposition, by which an arbitrary vector field is split up into a field with a so-called divergence constraint and an irrotational field. This leads to a fractional step scheme which consists of a predictor and a corrector step. The Poisson equation solved for the pressure in case of incompressible flows is extended to a Helmholtz equation for the computation of compressible flows. After solving the corrector step, the mass and momentum balances are fulfilled. This results in a fast numerical scheme, since no further iterations need to be computed. Based on the modified Helmholtz decomposition, it is shown that the created method can be understood as an extension of the incompressible projection scheme. Moreover, the spatial and temporal order of accuracy of incompressible projection-based methods are discussed and the ones of the compressible scheme are determined. The created compressible projection-based method is further on validated against a one-dimensional linear acoustic test case from the literature, whereby an analytical solution can be derived.

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A gas turbine model combustor is simulated with a hybrid, stochastic and particle-based method for combustion noise prediction with full 3D sound source modeling and sound propagation. Alongside, an incompressible LES simulation of the burner is considered for the investigation of the performance of the hybrid approach. The highly efficient time-domain method consists of a stochastic sound source reconstruction algorithm, the Fast Random Particle Method (FRPM) and sound wave propagation via Linearized Euler Equations (LEEs). In the context of this work, the method is adapted and tested for Combustion Noise (CN) prediction. Monopole sound sources are reconstructed by using an estimation of turbulence statistics from reacting CFD-RANS simulations. First, steady state and unsteady CFD calculations of flow field and combustion of the model combustor are evaluated and compared to experimental results. Two equation modeling for turbulence and the EDM (Eddy Dissipation Model) with FRC (Finite Rate Chemistry) for combustion are employed. In a second step, the acoustics simulation setup for the model combustor is introduced. Selected results are presented and FRPM-CN pressure spectra are compared to experimental levels.

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