UQ of 2D Slab Burner DNS: Surrogates, Uncertainty Propagation, and Parameter Calibration

TL;DR

The authors address uncertainty quantification for a complex 2D slab burner DNS by developing data-driven surrogates (Gaussian Processes and a Hierarchical Multiscale Surrogate) trained on an ensemble of DNS runs. They perform forward uncertainty propagation to the fuel regression rate and implement Bayesian calibration to update latent heat of sublimation and activation energy using experimental data, finding that DNS defaults underestimate these parameters. Across cross-validation, HMS outperforms GP in predictive accuracy, particularly for multiscale boundary quantities, and enables efficient forward UQ and calibration. The study demonstrates the importance of surrogate choice and parameter calibration for reliable UQ in combustion simulations and points to future work on higher-alkane fuels and time-varying QoIs for integrated predictive workflows.

Abstract

The goal of this paper is to demonstrate and address challenges related to all aspects of performing a complete uncertainty quantification analysis of a complicated physics-based simulation like a 2D slab burner direct numerical simulation (DNS). The UQ framework includes the development of data-driven surrogate models, propagation of parametric uncertainties to the fuel regression rate--the primary quantity of interest--and Bayesian calibration of the latent heat of sublimation and a chemical reaction temperature exponent using experimental data. Two surrogate models, a Gaussian Process (GP) and a Hierarchical Multiscale Surrogate (HMS) were constructed using an ensemble of 64 simulations generated via Latin Hypercube sampling. HMS is superior for prediction demonstrated by cross-validation and able to achieve an error < 15% when predicting multiscale boundary quantities just from a few far field inputs. Subsequent Bayesian calibration of chemical kinetics and fuel response parameters against experimental observations showed that the default values used in the DNS should be higher to better match measurements. This study highlights the importance of surrogate model selection and parameter calibration in quantifying uncertainty in predictions of fuel regression rates in complex combustion systems.

Figures (21)

• Figure 1: A sample temperature contour of the computational domain showing the specified inlet, outlet, isothermal wall, and fuel boundaries. The QoI is the time averaged regression rate at each point along the fuel boundary.
• Figure 2: Relative error in $\tilde{\tilde{\dot{r}}}$ as a function of the grid step size compared to the finest mesh size case ($\Delta x$ = 0.05 $mm$)
• Figure 3: Behavior of the basis functions centered at the same point at increasing scales ($s$). Reprinted with permission from SHEKHAR2022115760. Copyright 2022 Elsevier under Creative Commons License.
• Figure 4: Hyperparameter tuning for the HMS surrogate. $\delta$ describes the upper bound tolerance for the current scale tolerance ($\epsilon_s < \delta$), $s$ is the number of scales, and $k$ refers to a training data fold. Based on these results, we select $s = 21, \delta = 0.005$ for the two hyperparameters.
• Figure 5: Left: Effect of the most important Arrhenius parameters on ignition delay for our MMA mechanism. Right: Total sensitivity indices of the Arrhenius parameters of the four influential reactions identified by local sensitivity analysis. The parameters ($E_{257}, b_{249}, E_1, E_{250}$) are considered most important and are therefore part of the uncertain simulation ensemble.