A stochastic particle method for the investigation of turbulence/chemistry interactions in large-eddy simulations of turbulent reacting flows

The main objective of this work is to investigate the effects of the coupling between the turbulent fluctuations and the highly non-linear chemical source terms in the context of large-eddy simulations of turbulent reacting flows. To this aim we implement the filtered mass density function (FMDF) methodology on an existing finite volume (FV) fluid dynamics solver. The FMDF provides additional statistical sub-grid scale (SGS) information about the thermochemical state of the flow - species mass fractions and enthalpy - which would not be available otherwise. The core of the methodology involves solving a transport equation for the FMDF by means of a stochastic, grid-free, Lagrangian particle procedure. Any moments of the distribution can be obtained by taking ensemble averages of the particles. The main advantage of this strategy is that the chemical source terms appear in closed form so that the effects of turbulent fluctuations on these terms are already accounted for and do not need to be modeled. We first validate and demonstrate the consistency of our implementation by comparing the results of the hybrid FV/FMDF procedure against model-free LES for temporally developing, non-reacting mixing layers. Consistency requires that, for non-reacting cases, the two solvers should yield identical solutions. We investigate the sensitivity of the FMDF solution on the most relevant numerical parameters, such as the number of particles per cell and the size of the ensemble domain. Next, we apply the FMDF modeling strategy to the simulation of chemically reacting, two- and three-dimensional temporally developing mixing layers and compare the results against both DNS and model-free LES. We clearly show that, when the turbulence/chemistry interaction is accounted for with the FMDF methodology, the results are in much better agreement to the DNS data. Finally, we perform two- and three-dimensional simulations of high Reynolds number, spatially developing, chemically reacting mixing layers, with the intent of reproducing a set of experimental results obtained at the California Institute of Technology. The mean temperature rise calculated by the hybrid FV/FMDF solver, which is associated with the amount of product formed, lies very close to the experimental profile. Conversely, when the effects of turbulence/chemistry coupling are ignored, the simulations clearly over predict the amount of product that is formed.