A generalized partially stirred reactor model for turbulent closure

Abstract

A generalized Partially-Stirred Reactor (PaSR) model is presented in this work based on the inclusion of multiple chemical times. The PaSR model has shown promising results at modelling turbulence-chemistry interaction in Large-Eddy Simulations (LES) and Reynolds-Averaged Navier-Stokes (RANS), providing an extension of the well-known Eddy Dissipation Concept (EDC). PaSR model divides the computational domain into reactive and non-reactive parts. The factor defining this partition is expressed as a function of the system characteristic chemical and mixing times. However, the estimation of these factors, particularly the chemical one, is often oversimplified. The approach proposed in this study seeks to include in the PaSR model the whole set of chemical times involved in the reactive system. Besides, the concept of fine structures, first introduced in the EDC and often adopted also in the PaSR model to characterize the evolution of chemistry in the reactive part of the fluid, is here abandoned in favour of direct manipulation of species production rates. The mean source term is formulated according to the new generalized model through a modal decomposition of the Jacobian matrix. The method is validated a priori with DNS data of a syngas non-premixed jet flame, whose filtered data represent the validation benchmark. A good agreement is found between the new PaSR model and the filtered data for all species at different filter widths. Comparison with the single time scale based model clearly shows the limitations of the old standard approach and the necessity of including the whole spectrum of chemical times for a more comprehensive description of turbulence-chemistry interaction. A thorough analysis with the time scale participation index reveals the complexity of reaction rates contributions to the development of a specific time scale, underlying the importance of developing a model able to inherit all kinetic pathways in the turbulent closure.