The influence of Reynolds and Froude number on the local distribution of settling, inertial particles in turbulence

摘要

Particle-laden turbulent flows appear in a diverse range of engineering systems and natural phenomena and have been widely investigated in many theoretical, numerical and experimental studies. In this study, we employ Direct Numerical Simulations (DNS) to model turbulent flow, Lagrangian approach to track particles, and Voronoi tessellation analysis as the data processing technique to examine the effects of Taylor Reynolds number, R_λ ≡ u'λ/v (where u', λ and v denote the fluid r.m.s. velocity, the Taylor micro-scale and the fluid kinematic viscosity, respectively), and Froude number, Fr ≡ aη/g (where aη is the Kolmogorov acceleration, and g is the acceleration due to gravity), on the spatial distribution (clustering or preferential concentration) of small (sub-Kolmogorov scale), spherical, settling inertial particles (characterized by their Stokes number St ≡ τ_p/τ_η which is the ratio of the particle response time to the fluid timescale based on the Kolmogorov scale) in homogeneous isotropic turbulence. The appearance of clustering and its strength is diagnosed by exploring the distribution of Vorono'i volumes over a significant range of the three parameter space Fr = ∞, 0.3, 0.052, R_λ = 90, 224, 398 and 0 ≤ St ≤ 3 which are varied independently. In line with findings of previous studies using global measures of particle clustering, such as the Radial Distribution Function (RDF), we find that for small Vorono'i volumes (corresponding to the most concentrated regions of particles), the behavior depends strongly upon St and Fr, but only weakly upon R_λ unless St > 1. Furthermore, we observe a non-monotonic effect of gravity on St in which it decreases the clustering when St < 0(1) but increases the clustering for St ≥ 0(1) and this effect becomes more apparent at larger R_λ. Considering the properties of particles in clusters, defined as regions of connected Vorono'i cells whose volume is less than a certain threshold, we find that the statistics of the cluster volumes depends only weakly on St, with a stronger dependence on Fr and R_λ. Comparing the local dynamics of particles in clusters to all particles in the flow reveals that while their kinetic energies are nearly the same, the clustered particles settle much faster on average, and this difference grows significantly with increasing R_λ