Uncertainty quantification and sensitivity analysis of thermoacoustic stability with non-intrusive polynomial chaos expansion

• Published in: Combustion and flame Vol. 189; pp. 300 - 310
• Main Authors: Avdonin, Alexander, Jaensch, Stefan, Silva, Camilo F., Češnovar, Matic, Polifke, Wolfgang
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01-03-2018; Elsevier BV
• Subjects: Burners; Combustion chambers; Combustion dynamics; Compressibility; Computational efficiency; Computational fluid dynamics; Computer simulation; Configurations; Cost analysis; Equivalence ratio; Flow velocity; Helmholtz equations; Laminar flow; Mathematical models; Monte Carlo simulation; Parameter sensitivity; Parameter uncertainty; Polynomial chaos expansion; Polynomials; Reacting flow; Reflectance; Reflection; Sensitivity analysis; Stability analysis; Studies; Thermoacoustic instability; Thermoacoustics; Transfer functions; Uncertainty quantification; Uncertainty quantification; Sensitivity analysis; Thermoacoustics; Polynomial chaos expansion; Combustion dynamics; Thermoacoustic instability
• ISSN: 0010-2180; 1556-2921
• DOI: 10.1016/j.combustflame.2017.11.001

In this paper, non-intrusive polynomial chaos expansion (NIPCE) is used for forward uncertainty quantification and sensitivity analysis of thermoacoustic stability of two premixed flame configurations. The first configuration is a turbulent swirl combustor, modeled by the Helmholtz equation with an n−τ flame model. Uncertain input parameters are the gain and the time delay of the flame, as well as the magnitude and the phase of the outlet reflection coefficient. NIPCE is successfully validated against Monte Carlo simulation. It is observed that the first order expansion suffices to yield accurate results. The second configuration under investigation is a low order network model of a laminar slit burner, with the flame transfer function identified from weakly compressible CFD simulations of laminar reacting flow. Firstly the uncertainty and sensitivity of the growth rate due to three uncertain input parameters of the CFD model – i.e., flow velocity, burner plate temperature and equivalence ratio – are analyzed. A Monte Carlo simulation is no longer possible due to the computational cost of the CFD simulations. Secondly, two additional uncertain parameters are taken into account, i.e., the respective magnitudes of inlet and outlet reflection coefficients. This extension of the analysis does not entail a considerable increase in computational cost, since the additional parameters are included only in the low order network model. In both cases, the second order expansion is sufficient to model the uncertainties in growth rate.