The partially stirred reactor model for combustion closure in large eddy simulations: physical principles, sub-models for the cell reacting fraction, and open challenges

For their ability to account for finite-rate chemistry, reactor-based models are well suited Turbulence-Chemistry Interactions (TCI) Sub-Grid Scale (SGS) closures for Large Eddy Simulations (LES). The SGS closure in the Partially Stirred Reactor (PaSR) model relies on the determination of the reacting fraction of each computational cell, whose definition is based on estimates of the characteristic mixing and chemical time scales. Direct Numerical Simulations (DNS) of turbulent combustion can supply key information on TCI for the development, validation, and comparison of combustion models. In particular, a priori testing allows the direct validation of model assumptions. In the present work, an a priori assessment of the PaSR model is conducted. Its ability to reconstruct thermo-chemical quantities of interest is investigated along with model assumptions. Sub-grid quantities are extracted from the DNS to investigate the role of the cell reacting fraction. Various definitions are then proposed to estimate the characteristic chemical timescale in the PaSR model. Modeled chemical source terms and heat release rates are compared against the filtered quantities from DNS data of a two-dimensional, spatially developing, turbulent nonpremixed jet flame with detailed kinetics. The results demonstrate the importance of accounting for the fine structures quantities in the context of reactor-based models. A new formulation of the chemical timescale is proposed and provides improved overall predictions. Several issues are raised in the discussion, representing realistic prospects for further developments of the PaSR model as a SGS combustion closure for LES.