Autoignition flame transfer matrix: Analytical model versus large eddy simulations

Modern gas turbines need to fulfil increasingly stringent emission targets on the one hand and exhibit outstanding operational and fuel flexibility on the other. Ansaldo Energia GT26 and GT36 gas turbine models address these requirements by employing a combustion system in which two lean premixed combustors are arranged in series. Due to the high inlet temperatures from the first stage, the second combustor stage predominantly relies on autoignition for flame stabilization. In this paper, the response of autoignition flames to temperature, pressure and velocity excitations is investigated. The gas turbine combustor geometry is represented by a backward-facing step. Based on the conservation equations an analytical model is derived by solving the linearized Rankine-Hugoniot conditions. This is a commonly used analytical approach to describe the relation of thermodynamic quantities up- and downstream of a propagation stabilized flame. In particular, the linearized Rankine-Hugoniot jump conditions are derived taking into account the presence of a moving discontinuity as well as upstream entropy inhomogeneities. The unsteady heat release rate of the flame is modelled as a linear superposition of flame transfer functions, accounting for velocity, pressure, and entropy disturbances, respectively. This results in a 3 × 3 flame transfer matrix relating both primitive acoustic variables and the temperature fluctuations across the flame. The obtained analytical expression is compared to large eddy simulations with excellent agreement. A discussion about the contribution of the single terms to the modelling effort is provided, with a focus on autoignition flames.