Bayesian calibration of a methane-air global scheme and uncertainty propagation to flame-vortex interactions

Abstract

Simplified chemistry models are commonly used in reactive computational fluid dynamics (CFD) simulations to alleviate the computational cost. Uncertainties associated with the calibration of such simplified models have been characterized in some works, but to our knowledge, there is a lack of studies analyzing the subsequent propagation through CFD simulation of combustion processes.This work propagates the uncertainties -arising in the calibration of a global chemistry model -through direct numerical simulations (DNS) of flame-vortex interactions. Calibration uncertainties are derived by inferring the parameters of a two-step reaction mechanism for methane, using synthetic observations of one-dimensional laminar premixed flames based on a detailed mechanism. To assist the inference, independent surrogate models for estimating flame speed and thermal thickness are built taking advantage of the Principal Component Analysis (PCA) and the Polynomial Chaos (PC) expansion. Using the Markov Chain Monte Carlo (MCMC) sampling method, a discussion on how push-forward posterior densities behave with respect to the detailed mechanism is provided based on three different calibrations relying (i) only on flame speed, (ii) only on thermal thickness, and (iii) on both quantities simultaneously.The model parameter uncertainties characterized in the latter calibration are propagated to two-dimensional flamevortex interactions using 60 independent samples. Posterior predictive densities for the time evolution of the heat release and flame surface are consistent, being that the confidence intervals contain the reference simulation. However, the twostep mechanism fails to reproduce the flame response to stretch as it was not considered in the calibration. This study highlights the capabilities and limitations of propagating chemistry-models uncertainties to CFD applications to fully quantify posterior uncertainties on target quantities.

Uncertainty quantification analysis of Reynolds-averaged Navier–Stokes simulation of spray swirling jets undergoing vortex breakdown

“…In this regard, Figure 13 illustrates the field distribution of the first-order Sobol index for ω d as concerns the different values of Ψ, accompanied with the variance of Y v , as computed from equation (23). In the first place, it must be noted that the variance of Y v remains mostly concentrated in the near-field mixing layer and the far-field vortex core, regardless of the liquid mass loading.…”

“…More specifically, reference data provided experimentally or via DNS, if available, may be exploited to perform an inverse UQ analysis, which returns a representation of the uncertain parameters in terms of probability density functions (PDFs), that allow for a complete exploration of the input space. [20][21][22][23] Once the PDFs are known, the submodel uncertainty may be propagated to the QoIs through low-fidelity RANS simulations, employing a polynomial chaos expansion (PCE) representation of the random variables (RVs) being involved to reduce the number of required simulations. [24][25][26][27][28] This way, CFD results become supported by reliability measures, such as error bars or confidence intervals, similar to the usually adopted representations of experimental results.…”