A general probabilistic approach for the quantitative assessment of LES combustion models

Abstract

The Wasserstein metric is introduced as a probabilistic method to enable quantitative evaluations of LES combustion models. The Wasserstein metric can directly be evaluated from scatter data or statistical results using probabilistic reconstruction against experimental data. The method is derived and generalized for turbulent reacting flows, and applied to validation tests involving the Sydney piloted jet flame. It is shown that the Wasserstein metric is an effective validation tool that extends to multiple scalar quantities, providing an objective and quantitative evaluation of model deficiencies and boundary conditions on the simulation accuracy. Several test cases are considered, beginning with a comparison of mixture-fraction results, and the subsequent extension to reactive scalars, including temperature and species mass fractions of CO and CO 2 . To demonstrate the versatility of the proposed method in application to multiple datasets, the Wasserstein metric is applied to a series of different simulations that were contributed to the TNF-workshop. Analysis of the results allowed to identify competing contributions to model deviations, arising from uncertainties in the boundary conditions and model deficiencies. These applications demonstrate that the Wasserstein metric constitutes an easily applicable mathematical tool that reduce multiscalar combustion data and large datasets into a scalar-valued quantitative measure.

Requirements Towards Predictive Simulations of Turbulent Combustion

“…Recently, the Wasserstein metric was introduced as a generalized measure for the quantitative evaluation of combustion models. 31 Compared to commonly employed techniques that consider loworder statistical moments, this metric is formulated in distribution space, which enables the direct consideration of instantaneous data that are obtained from transient simulations and high-speed measurements without the need for data reduction to low-order statistical moments. This metric is able to incorporate multidimensional data into a scalar-valued quantity, thereby aggregating model discrepancies for individual quantities.…”

“…The Wasserstein metric has been employed to assess different modeling approaches in simulating a turbulent jet flame with inhomogeneous inlets. 31,32 Representative results are illustrated in fig. 5, showing comparisons of the multiscalar Wasserstein metric for QoIs of mixture fraction, temperature, and species mass fractions of CO 2 and CO.…”

“…The Wasserstein metric has been employed to assess different modeling approaches for simulating turbulent flames [63,69,71]. Representative results are illustrated in Fig.…”

Towards affordable Uncertainty Quantification in the Simulation of Turbulent Spray Combustion via Surrogate Modeling

“…While surrogate model based uncertainty quantification has been demonstrated for gaseous combustion simulations [6][7][8], only few studies are available on reacting multiphase flow. Gel et al [9] used a Multivariate Adaptive Regression Spline (MARS) surrogate model to study uncertainties in the simulation of a fluidized bed gasifier.…”

Mind the gap: Turbulent combustion model validation and future needs

“…Quantitative comparison of multiscalar Wasserstein metric as a measure of global error[188], from ten anonymized LES-calculations, presented at the 13th TNF-workshop[115] for flame conditions FJ-5GP-Lr75-57 in the inhomogenous flame[72][73][74][75]. The decomposition of multiscalar calculations allows contributions from each variable at each axial location to become visible.…”