Multi-particle models of molecular diffusion for Lagrangian simulation coupled with LES for passive scalar mixing in compressible turbulence

Abstract

Lagrangian simulation coupled with large eddy simulation (LES) is studied for turbulent scalar mixing in compressible flows, where Lagrangian simulation solves advection-diffusion equations with computational particles. In Lagrangian simulation, a molecular diffusion term needs to be modeled with a so-called mixing model, which also requires modeling the dissipation rate of scalar fluctuations. The present study extends a particle-based subgrid-scale model for the scalar dissipation rate to compressible flows, and its validity in compressible turbulence is examined with direct numerical simulation databases of a temporally evolving turbulent planar jet with a jet Mach number of 0.6 or 1.6. A priori test confirms that the model can well predict the mean scalar dissipation rate in the subsonic and supersonic turbulent jets. The model hardly depends on the spatial distribution of the particles when the number of particles used in the model is about 12. However, the scalar dissipation rate tends to be overestimated by the model in regions with large dilatation fluctuations although such regions with strong compressibility effects occupy only a small part of the flow. Lagrangian simulation coupled with LES of the turbulent jet is also performed with the scalar dissipation model combined with the mixing volume model. Lagrangian simulation with these models effectively predicts passive scalar statistics, such as averages, rms fluctuations, and turbulent fluxes, in the turbulent jet with both subsonic and supersonic jet velocities. The scalar dissipation model well predicts the coarse-grained scalar dissipation rate in Lagrangian simulation. The present results confirm that the mixing volume model combined with the particle-based model of the scalar dissipation rate is useful in Lagrangian simulation coupled with LES, which is a promising approach for simulating high-speed turbulent reacting flows as reaction terms appear in Lagrangian simulation in a closed form.