Uncertainty quantification of thermo-acoustic instabilities in annular combustors

Abstract

An Uncertainty Quantification (UQ) method based on active subspace and low-order models is applied on a simplified gas turbine to determine its modal risk factor: the probability of an acoustic mode to be unstable. The configuration is a simplified 19-burner annular combustor which is operated in two different regimes, called weakly and strongly coupled regimes. Each flame is modeled by two uncertain parameters leading to a large UQ problem involving 38 parameters. The combustor is modeled as a network of 4 × 19 1D interconnected 1D acoustic elements which is efficiently solved quasi-analytically (ATACAMAC) as proposed recently by Bauerheim et al. (2014b). This allows us to perform a Monte Carlo analysis (approx. 10, 000 ATACAMAC calculations), assuming that the uncertainties on the inputs are known. The reference Monte Carlo risk factor is then compared with that obtained by a less demanding UQ method. First, the dimension of the problem is reduced from 38 to only 3 parameters for the two regimes considered by the active subspace approach based on gradient correlations. Then, linear and quadratic analytical models based on the three active variables are fit using 100 ATACAMAC simulations. These low-order models are then replayed 100, 000 times to obtain the PDF of the growth rate as well as the risk factor estimation. Results show that for both regimes, the UQ method is able to accurately predict the risk factor of the configuration.