Clustering model for Partially Stirred Reactor closures: Application to Cabra jet flames

In the field of turbulent reacting flows, combustion phenomena, such as the mixing of cold fuel with hot products, propagation of flames, and auto-ignition, are profoundly affected by interactions between turbulence and chemistry, known as turbulence-chemistry interactions (TCI). Accurately modeling these intricate combustion processes requires a closure adept at capturing TCI behavior. Among the existing combustion models, the Partially Stirred Reactor (PaSR) model, as one of the finite-rate chemistry models, has shown significant suitability for modeling TCI within various combustion regimes. The modeling of chemical and mixing time scales is crucial to the performance of the PaSR model. Although numerous studies have extensively explored these aspects in separate efforts, there is a notable lack of a systematic study on employing the PaSR model to turbulent flames with multiple combustion regimes. In the present study, the Cabra flame, a vitiated coflow flame with multiple combustion regimes, is investigated by using large eddy simulations (LES) coupled with the PaSR model. Particular emphasis is placed on evaluating the combinations of the chemical and mixing time scales. Twelve combinations, involving three distinct chemical time scales and four different mixing time scales, are evaluated. The results reveal that both the chemical and mixing time scales significantly influence the model’s predictive accuracy, and various combinations exhibit varied predictive strengths in flame transition and diffusion regions. Based on the findings from these twelve combinations, a clustering model for Partially Stirred Reactor closure is first proposed. The model performance is then assessed, showing a better prediction in mean and root mean square values of temperature and species concentrations, as well as probability density functions of the reaction fraction, as compared to the traditional PaSR models.