Multiple representative interactive linear eddy model: Investigation of turbulence chemistry interaction and evaluation of progress variable definition and PDFs

Improving the predictions of unsteady effects in combustion processes requires novel combustion models that include turbulence chemistry interaction effects. The Multiple Representative Interactive Linear Eddy Model (MRILEM) is an improved version of the previous RILEM variant. MRILEM utilizes a pressure coupling instead of a volume constraint to intrinsically include heat effects into the LEM line with no supplementary modeling. In addition, it advances multiple LEM lines in parallel to improve statistical fidelity. The pressure coupling of MRILEM generates a coupling effect between the LEM lines that assists in communicating the combustion process between the lines. The ”Spray-B” engine of the Engine Combustion Network (ECN) was simulated using MRILEM. While the original RILEM variation employs a straightforward Dirac $\delta$-peak for the progress variable, a realistic PDF requires this function to extend over the entire space. The introduced MRILEM compares the utilization of two progress variable PDFs, namely a step function defined based on the mean and a $\beta$-PDF generated from the progress variable mean and variance. The progress variable variance was calculated based on the Pierce and Moin formulation with a RANS adaptation based on the integral length scale. In addition, two definitions of the progress variable are investigated, namely $O_2$ and $h_{298}$. A tabulation method is introduced for RILEM to reduce the computational time by advancing pre-generated LEM solution matrices constructed in mixture fraction $Z$ and progress variable $c$ spaces. The different variants of the model, i.e., MRILEM-${\beta }_Z$-Step${}_c$, MRILEM-${\beta }_Z$-${\beta }_c$, TRILEM-${\beta }_Z$-${\text{Step}}_c$, and TRILEM-${\beta }_Z$-${\beta }_c$ were compared against experiments based on heat release rate, ignition delay, flame lift-off, and computational time.