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On convergence of moments in uncertainty quantification of combustion simulations

We summarise the results of a computational study involved with Uncertainty Quantification (UQ) in reacting-flow combustion simulations. Results of UQ in simulations of a well characterised lab-scale turbulent burner flame and a theoretical laminar flame front based on Monte Carlo (MC) sampling and Polynomial Chaos Expansion (PCE) techniques are presented and examined. The convergence characteristics of both methods are quantified, compared and discussed. Quantifying uncertainty in cases with laminar and turbulent flows reveals a relationship between the PCE's convergence behaviour and the system dynamics. It is found that if the impact of uncertainty in a system input translates to a system response of low standard deviation, signifying a chaotic response, the performance characteristics of PCE reduce to a level where its convergence rate is comparable to MC. The results demonstrate that it is ineffective to adopt the PCE methodology when quantifying uncertainty in combustion simulations on default basis, which is a widespread practise, because of the complexity associated with technique's implementation and the assumptions it makes about the nature of the system response. In particular we found that, within a certain flow regime, there exists a power-law relationship between a comparative parameter defined to distinguish between the convergence rates of PCE and MC that scales with the standard deviation of the system response quantity of interest. The existence of this correlation is of substantial practical relevance. It constitutes a criterion for guiding the selection of the appropriate technique to quantify uncertainty in combustion simulations of the type addressed here.