Intrinsic filtering errors of Lagrangian particle tracking in LES flow fields

Abstract

1 Large-Eddy Simulations (LES) of two-phase turbulent flows exhibit quantitative differences in particle statistics if compared to Direct Numerical Simulations (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 subgrid-scale velocity field on the force driving the particles, and establish the requirements which a LES model must satisfy to predict correctly the velocity and the trajectory of inertial particles.2

Lagrangian filtered density function for LES-based stochastic modelling of turbulent particle-laden flows

“…Given the accuracy of the spectral method, such a comparative validation represents a robust way to assess the performance of the LFMDF solution provided by the Monte Carlo simulation. We are particularly interested in examining the particle velocity statistics, but also the particle number density distribution, which is the macroscopic result of turbophoresis [23,55] and (25)- (27), with those of the Eulerian pseudo-spectral simulation, which solves for Eqns. (1)- (2).…”

“…These flaws have obvious consequences on the applicability of LES to industrial processes and environmental phenomena such as mixing, combustion, depulveration, spray dynamics, pollutant dispersion, or cloud dynamics [25]. Recent analyses based on Direct Numerical Simulation (DNS) of turbulence have also shown that neither deterministic models nor stochastic homogeneous models have the capability to correct fully the inaccuracy of the LES approach due to SGS filtering [26][27][28][29]. Prompted by the abovementioned findings, some attempts have been made on a heuristic ground, both for isotropic [30][31][32][33] and wall-bounded flows [34,35].…”

Numerical and experimental analysis of vertical spray control patternators

“…The rationale behind LES can be summarized saying that momentum, mass, energy, and other passive scalars are transported mostly by large eddies, although some problems arise when particles or droplet interacts with the filtered flow field (Bianco et al, 2012). Large eddies are related to the geometries and boundary conditions of the modeled flow, while small eddies tend to be more isotropic, and are consequently more universal.…”

Hydrodynamic force and torque models for a particle moving near a wall at finite particle Reynolds numbers

“…They also used the repulsive force between the particle surfaces when the gap is less than a critical value. In current large-eddy simulation of particle-laden channel flows, the unresolved sub-grid scale motion might affect the particle-wall interaction ( Bianco et al, 2012 ). The contributions of the sub-grid scale fluid motions on particle-wall interaction can be partially modeled by constructing particle sub-grid scale model based on the space-time correction theory ( He et al, 2002;Yang et al, 2008;Zhao and He, 2009 ).…”