Particle tracking in LES flow fields: conditional Lagrangian statistics of filtering error

Abstract

In this paper, we examine the conditional Lagrangian statistics of the pure filtering error, which affects particle tracking in large-eddy simulations of wall-bounded turbulence. A-priori tests are performed for the reference case of turbulent channel flow, and statistics are computed along the trajectory of many particles with different inertia, initially released in near-wall regions where either a sweep event or an ejection event is taking place. It is shown that the Lagrangian probability density function (PDF) of the filtering error is, in general, different from the Eulerian one, computed at fixed grid points. Lagrangian and Eulerian PDFs become similar only in the long-time limit, when the filtering error distribution is strongly non-Gaussian and intermittent. Results also show that the distribution of the short-time error in the homogeneous directions can be approximated by a Gaussian function. Due to flow anisotropy effects, which are particularly significant for small-inertia particles, such approximation does not hold in the wall-normal direction.

Keywords:

• large-eddy simulation
• Lagrangian sub-grid modeling
• turbulent dispersed flows

Acknowledgements

COST Actions FP1005 and MP0806 are gratefully acknowledged.

Notes

1. If in an LES the equation of particle motion is solved with the filtered fluid velocity, three sources of error can be distinguished with respect to DNS [9]. The filtering (or subgrid) error is introduced because equations are solved with the filtered velocity. Second, a modelling error occurs because a real LES does not provide the exact filtered velocity to the particle equations, but only an approximation due to the limitations of the sub-grid model. Third, an interpolation error is made, since the LES is performed on a much coarser grid than the DNS. However, this error can be considered negligible when high-order interpolation schemes are used [9].