Intrinsic filtering errors of Lagrangian particle tracking in LES flow fields

Large-eddy simulation (LES) of two-phase turbulent flows exhibits quantitative differences in particle statistics if compared to direct numerical simulation (DNS) which, in the context of the present study, is considered the exact reference case. Differences are primarily due to filtering, a fundamental intrinsic feature of LES. Filtering the fluid velocity field yields approximate computation of the forces acting on particles and, in turn, trajectories that are inaccurate when compared to those of DNS. In this paper, we focus precisely on the filtering error for which we quantify a lower bound. To this aim, we use a DNS database of inertial particle dispersion in turbulent channel flow and we perform a priori tests in which the error purely due to filtering is singled out removing error accumulation effects, which would otherwise lead to progressive divergence between DNS and LES particle trajectories. By applying filters of different type and width at varying particle inertia, we characterize the statistical properties of the filtering error as a function of the wall distance. Results show that filtering error is stochastic and has a non-Gaussian distribution. In addition, the distribution of the filtering error depends strongly on the wall-normal coordinate being maximum in the buffer region. Our findings provide insight on the effect of sub-grid scale velocity field on the force driving the particles, and establish the requirements that any closure model aimed at recovering sub-grid scale effects on the dynamics of inertial particles must satisfy.