Pitfalls Measuring 1D Inertial Particle Clustering

Abstract

Clustering is an important phenomenon in turbulent flows laden with inertial particles. Although this process has been studied extensively, there are still many 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, that can enable high resolution modeling.In this work, we study the effect of projecting this phenomenon onto 2D and 1D (as usually done in experimental measurements). 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 and 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 (η), and smaller than about ten percent of the integral length scale of the turbulence L. This dependency provides the correct scaling to carry out unidimensional measurements of preferential concentration, taking into account the turbulence characteristics.Additionally, it is critical to disentangle the cluster-characterizing results from random contributions to the cluster statistics, specially in 1D, as the raw probability density function (PDF) of Voronoï 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 (RPP) probability distribution in 1D, which appears to discard the existence of power laws in the cluster PDF. At higher dimensions, 2 or 3 D, power law tails were found with our cluster identification algorithm. 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.

Effect of Reλ and Rouse numbers on the settling of inertial droplets in homogeneous isotropic turbulence

“…In this work, we refrained from analyzing the preferential concentration from 1D particle records, for instance via 1D Voronoï tessellations [44], as a previous work from the group suggests that these statistics in our experimental setup may present biases that could lead to misleading conclusions see [45]. Nonetheless, the presence of clusters (higher density regions with respect to the average concentration) and voids (lower density regions with respect to the average concentration) may be of relevance in this problem.…”

Buoyancy-driven bubbly flows: role of meso-scale structures on the relative motion between phases in bubble columns operated in the heterogeneous regime

“…The key points in figure 3(b) are the very sharp increase in σ voronoi observed at the homogeneous-heterogeneous transition, and the large value, well above that of an RPP, that σ voronoi reaches at high V sg . The shortcomings of 1-D Voronoï analysis in complex flows have been discussed elsewhere (Mora et al 2018(Mora et al , 2019: one key result is that the clear difference observed with the standard deviation of an RPP unambiguously demonstrates that clustering does occur in the present flow conditions. Furthermore, for all heterogeneous conditions investigated (that is, for V sg up to 24 cm s −1 ), the standard deviation σ voronoi remains nearly the same: that feature also indicates that clustering is a central characteristic of the heterogeneous regime.…”

“…Paralleling what we did for turbulent particle-laden flows (Monchaux, Bourgoin & Cartellier 2010;Sumbekova et al 2017;Mora et al 2018), we exploit 1-D Voronoï tessellations built from the gas phase indicator function X G (t) (Raimundo 2015;Mezui, Cartellier & Obligado 2018;Raimundo et al 2019). Here, X G (t) is deduced from the signal delivered by an optical probe.…”

“…To quantify the connection between cell width T k / T k and concentration, we consider two approaches. First, we follow what we did for a turbulent flow laden with droplets (Sumbekova et al 2017;Mora et al 2018), by connecting the ratio T k / T k to linear number densities, i.e. with the number of inclusions detected per unit length.…”

Experimental estimation of turbulence modification by inertial particles at moderateReλ

“…Just downstream of it, a rack of spray nozzles produced polydisperse inertial water droplets [21]. This wind tunnel has been extensively used to study particle-turbulence interaction under homogeneous isotropic turbulent (HIT) conditions (more experimental details are described in [22][23][24]). The measuring station was located three meters (3m) downstream the active grid, and at the center line of the wind tunnel, where HIT and the classical scalings from K41 theory have been recovered [15].…”