  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.
