Localized conditional source-term estimation model for turbulent combustion

A novel functional form for approximating the conditional scalars in turbulent reacting flows is introduced based on the Bernstein polynomial. Multi-scalar measurement data of turbulent premixed and non-premixed flames are used to demonstrate that the new functional form provides an excellent reduced-order model for the conditional scalars. This model order reduction technique can be used to improve the accuracy, reduce the computational cost and enhance the spatial localization of the Conditional Source-term Estimation (CSE) model. CSE is a turbulence-chemistry interaction model similar to the Conditional Moment Closure (CMC) model, except that the conditional scalars are estimated from the filtered field in an ensemble of LES cells using an integral equation. An a priori analysis using the DNS data of a series of statistically planar turbulent premixed flames shows that using Bernstein polynomials as the presumed functional form for the conditional scalars provides better regularization than the conventional CSE approach. Furthermore, the ensemble size – that was previously kept on the order of thousands of LES cells in the singly-conditioned CSE – can be reduced to as low as 16 LES cells. This enhanced localization approach reduces the modelling error and the computational cost compared to the conventional CSE approach for tabulated and reduced chemistry models.