Different conditional source-term estimation formulations applied to turbulent nonpremixed jet flames with varying levels of extinction

The objective of the present study is to investigate two new formulations of the Conditional Source-term Estimation (CSE) model using Reynolds Averaged Navier Stokes (RANS) calculations applied to Sandia flames D and F. The first method relies on a first-order Tikhonov regularisation and the second approach denoted by CSEBP, includes Bernstein polynomials to approximate the conditional averages. Current predictions for temperature, main product and minor species are consistent with previously published CSE results with a different implementation. However, smoother conditional profiles are obtained with less a priori information. Both formulations have good predictions for flame D with minor discrepancies near the inlet and one position downstream, with occasional small advantages for CSEBP. In contrast to previous RANS-CSE attempts, stable solutions are obtained for flame F in good agreement with the experiments. Considering the RANS and single conditioning limitations to capture transient effects, both formulations predict the changes of conditional averages and Favre averaged quantities from flame D to F well, except at one location where the predicted re-ignition occurs earlier than what is seen in the experiments. Additionally, the computational cost of the CSE routine is decreased significantly from $ 85\% $ 85 % of the total computational cost to only $ 10\% $ 10 % for the first formulation and under $ 3\% $ 3 % for CSEBP by means of using hash tables for storing the results of interpolations from the chemistry tables and avoiding on-the-fly interpolations.