Characterizing inertial particle clustering with 1D signals

Abstract

Preferential concentration in turbulent flows laden with inertial particles still presents many open fundamental physics questions. These gaps hinder the reconciliation of different experimental and numerical studies into a coherent quantitative view, which is needed to enable accurate high resolution modeling. We examine the influence of the dimensionality of the measurement technique (1D line, 2D planes or 3D volumes) on the characterization of cluster properties/preferential concentration, and proposes an approach to disentangle the cluster-characterizing results from random contributions that could contaminate the cluster statistical analysis. We studied this effect by projecting 2D and 3D data snapshots containing inertial particle clusters onto a 1D axis. The objective was to simulate 1D sensors (widely used experimentally: hot wire, fiber optics probes, LDV/PDA, etc) with different sensing lengths. These projected records were analysed by means of one-dimensional Voronoï tessellations. For the experimental parameters explored in this study, our results retrieved average clustering properties, when the measuring window is equal or larger than the Kolmogorov length scale (η), and smaller than of the integral length scale of the turbulence . These observations are consistent with previous research using 2D and 3D datasets taken under similar experimental conditions. The raw probability density function (PDF) of the Voronoï length in 1D does not provide error-free information on the clusters size or local concentration. This measurement bias is corrected based on the histograms of the number of particles within each cluster. Importantly, the analysis of these histograms explains the well-known clusters size PDFs power law reported in previous numerical and experimental research using 2D and 3D datasets. This power-law behavior, however, spanning less than a decade, is not robust in 1D. To address this, we use conditioned statistics (on the number of particles inside each cluster) to discern between turbulence-driven clustering and random particle concentration fluctuations. This secondary analysis complements standard cluster identification algorithms that rely on Voronoï tessellations.