Characterizing 1D Inertial Particle Clustering

TL;DR

This paper investigates how 1D and 2D measurements of inertial particle clustering in turbulence are affected by measurement volume, proposing correction methods and scaling laws to improve the accuracy of experimental and numerical observations.

Contribution

It introduces a methodology to correct measurement bias in 1D clustering data and provides scaling laws for measurement volume relative to turbulence scales.

Findings

Measurement volume should be between Kolmogorov and 10% of integral length scale.

A correction method for measurement bias in 1D cluster statistics is proposed.

Discards power-law assumptions in cluster PDF, favoring a Poisson-based model.

Abstract

Clustering is an important phenomenon in turbulent flows laden with inertial particles. Although this process has been studied extensively, there are still open questions about both the fundamental physics and the reconciliation of different observations into a coherent quantitative view of this important mechanism for particle-turbulence interaction. In this work, we study the effect of projecting this phenomenon onto 2D and 1D (as usually done in experiments). In particular, the effect of measurement volume in 1D projections on detected cluster properties, such as size or concentration, is explored to provide a method for comparison of published/future observations, from experimental or numerical data. The results demonstrate that, in order to capture accurate values of the mean cluster properties under a wide range of experimental conditions, the measurement volume needs to be larger than the Kolmogorov length scale, and smaller than about ten percent of the integral length scale of the turbulence. This dependency provides the correct scaling to carry out 1D measurements of preferential concentration, considering the turbulence characteristics. It is also critical to disentangle the cluster-characterizing results from random contributions to the cluster statistics, especially in 1D, as the raw probability density function of Voronoi cells does not provide error-free information on the clusters size or local concentration. We propose a methodology to correct for this measurement bias, with an analytical model of the cluster PDF obtained from comparison with a Random Poisson Process probability distribution in 1D, which appears to discard the existence of power laws in the cluster PDF. We develop a new test to discern between turbulence-driven clustering and randomness, that complements the cluster identification algorithm by segregating the number of particles inside each cluster.