Velocity and acceleration statistics in particle-laden turbulent swirling flows

Abstract

We present a comparison of different particles' velocity and acceleration statistics in two paradigmatic turbulent swirling flows: the von Kármán flow in a laboratory experiment, and the Taylor-Green flow in direct numerical simulations. Tracers, as well as inertial particles, are considered. Results indicate that, in spite of the differences in boundary conditions and forcing mechanisms, scaling properties and statistical quantities reveal similarities between both flows, pointing to new methods to calibrate and compare models for particles dynamics in numerical simulations, as well as to characterize the dynamics of particles in simulations and experiments. The comparison also allows us to identify contributions of the mean flow to the inertial range scaling of the particles' velocity structure functions.

Dynamic mode decomposition of inertial particle caustics in Taylor–Green flow

“…We propose that the DMD technique can be used to analyze real experimental PIV data of caustics and perform similar analysis to extract information about the Stokes numbers and concentrations of the particles. In future we will consider detailed Navier-Stokes equation for the self-consistent evolution of the velocities and analyze the caustic structures in 3D 39 and turbulent flows 18 , 40 . Contrary to the Taylor-Green flow case, a single dominant DMD mode does not capture the complete features of the caustics in a turbulent flow.…”

Broken Mirror Symmetry of Tracer’s Trajectories in Turbulence

“…The eight cells are labeled as [C x ,C y ,C z ], where C i ¼ 1 or 2, with 1 labeling the region from 0 to π in the ith direction, and 2 the region between π and 2π (i.e., the cell labeled [1,2,1] refers to the subregion ½0; πÞ × ½π; 2πÞ × ½0; πÞ of the whole computational domain). Each cell has a flow that in many previous studies was shown to have Eulerian and Lagrangian similarities with that observed in VK experiments [39,40,45], despite differences in boundary conditions and forcing mechanisms (volumetric forcing in the former, and two counterrotating propellers in the latter): two counterrotating vortices separated by a shear layer. The VK flow has nonzero helicity, while given the TG symmetries, four of the DNS cells have mean helicity with a preferential sign, and the other four cells have the opposite sign.…”

“…In each simulation 10 6 tracers were evolved along with the fluid. Experimental data on tracers trajectories obtained by PTV originates from two experiments: a VK experiment in Buenos Aires [40] generates a helical flow, and the Lagrangian Exploration Module (LEM) in Lyon [41,42] generates mirror-symmetric isotropic turbulence.…”

Multi-time structure functions and the Lagrangian scaling of turbulence

“…Tracers' velocity structure functions are known to display short ranges compatible with Kolmogorov scaling, with an amplitude and width that grows slowly with the Reynolds number [7][8][9][10]. Furthermore, large-scale flows have been found to affect both small-scale Lagrangian and Eulerian turbulent statistics [11][12][13][14][15]. More recently, long Lagrangian trajectories were shown to retain information of the large-scale flow topology [16].…”