Network- and CFD/CAA-modelling of the high frequency flame response in multi-jet combustors

Low order networks are widely used for linear stability analysis of combustors in the low frequency limit. High frequency stability analysis, however, is limited to cost-intensive numerical or experimental methods, since derivation of analytical solutions is either cumbersome or impossible. The article at hand provides a quasi-two-port network model for the effective modal acoustic pressure and axial velocity normalised with the transverse acoustic field for cylindrical combustors. This network modelling approach includes transfer matrices of acoustic area jumps, ducts for longitudinal, standing and spinning transverse and mixed mode wave propagation. The purely acoustic transfer matrices are validated with a generic non-reactive experiment. On the basis of phase-locked (Formula presented.) images of an engine-similar multi-jet combustor with a forced T1 mode, a locally distributed flame response model is derived, which is reduced to a global flame transfer matrix. A locally resolved convective flame response model is implemented in a numerical model in order to verify the provided theory by the comparison of the analytical and numerical flame transfer matrix for the high-frequency regime.