58352 - Confidence in Flame Impulse Response Estimation From Les With Uncertain Thermal Boundary Conditions 

Combustion instabilities are a major cause of concern in the development of gas turbine engines. Hence, there is a need to predict the occurrence of these instabilities during the design phase with simulation tools. Thermoacoustic network models are low computational cost tools that estimate the growth rate of the eigenmodes of the system. These models require information on the flame dynamic response. The combined approach of advanced System identification (SI) and Large Eddy Simulation (LES), externally forced with a carefully designed broadband signal, is an efficient strategy to compute the flame dynamic response to flow perturbation via Finite Impulse Response (FIR). The identified FIR is uncertain due in part to the statistical nature of the estimation procedure (for e.g. low signal-to-noise ratio or finite length of time series) and partly due to uncertainty in the CFD simulation itself caused by uncertain boundary conditions. Carrying out traditional uncertainty quantification techniques, such as multi-layer Monte Carlo, in the framework LES/SI would be computationally prohibitive. As a result, the present paper proposes a surrogate based framework to quantify the uncertainty in the FIR model caused by the joint uncertainty that stems from System Identification on the one hand and boundary conditions in LES on the other. More specifically, we propose a bootstrapping Gaussian Process (GP) surrogate model where in the final trained GP uncertainty contains the uncertainty of SI and the uncertainty in the combustor back plate temperature, which is known to have considerable impact on the Flame Transfer Function. The GP model is trained on the FIRs obtained from the LES/SI of turbulent premixed swirled combustor at different combustor back plate temperatures. Due to the change in the combustor back plate temperature the flame topology changes, which in turn influences the FIR. The trained GP model is successful in interpolating the FIR with confidence intervals covering the “true” FIR from LES/SI.