Supervised clustering for optimal sub-model selection in reactor-based models

Reactor-based models are well-suited Turbulence-Chemistry Interactions, Sub-Grid Scale closures for Large Eddy Simulation (LES) due to their ability to account for finite-rate kinetics. The Partially Stirred Reactor (PaSR) model relies on the estimation of charac- teristic time scales to define the reacting fraction of each computational cell. However, chemistry develops a spectrum of intrinsic chemical time scales, leaving no clear consen- sus on the definition of a single representative scale. Nevertheless, in numerical codes, a single chemical time scale formulation is used on the whole physical domain despite local and complex phenomena. Through an a priori assessment on Direct Numerical Simulation (DNS) data of turbulent non-premixed combustion, the present work proposes a numeri- cal method to locally select an optimal chemical time scale formulation that minimises the model error. Data points are grouped into clusters via supervised partitioning algorithms where the optimal formulation is attributed to each cluster by means of distances minimisa- tion. Using a combination of partitioning procedures can further improve the reconstruc- tion quality of the clustered solutions, up to 35% global errors reductions with respect to standard solutions. Existing data partitions are then tested on unseen data points, yielding great prediction capabilities. DNS data of a turbulent premixed flame are used to demon- strate that the methodology is also robust across combustion regimes. The present proof of concept shows suitable features to introduce systematic improvements for the PaSR com- bustion closure in LES.