Multi-particle model of coarse-grained scalar dissipation rate with volumetric tensor in turbulence

Abstract

A multi-particle model is proposed for a coarse-grained scalar dissipation rate, where a coarse-grained quantity is defined with an ensemble average of spatially-distributed fluid particles within a finite volume. The model computes the coarse-grained scalar dissipation rate from the coarse-grained scalar gradient with a subgrid scale model of the scalar dissipation rate, which requires length-scale estimation for particle distribution. A volumetric tensor that characterizes the particle distribution is used in the model for computing the length scale and the coarse-grained scalar and velocity gradients from the particles. The model is examined in a priori and posteriori tests. A priori test with direct numerical simulation (DNS) databases of turbulent planar jets shows that the present model works well for a wide range of the length scale of particle distribution when the number of particles NM is about 10-16. The model with NM≲10 overestimates the coarse-grained scalar dissipation rate, while NM≳16 causes stronger dependence of the model on the length scale of particle distribution. The proposed model is tested in hybrid large-eddy-simulation/Lagrangian-particle-simulation (LES/LPS) of planar jets, where the coarse-grained scalar dissipation rate appears as an unknown variable in a mixing volume model that computes a molecular diffusion term based on a multi-particle interaction. LES/LPS and DNS yield a similar profile of the root-mean-squared scalar fluctuation, which strongly depends on the scalar dissipation rate. Comparison of the mean scalar dissipation rate between the model and the DNS shows that the present model applied to the LES/LPS well predicts the coarse-grained scalar dissipation rate at various jet Reynolds numbers.