Abstract
This paper deals with the numerical analysis of the particle inertia and volume fraction effects on colliding particle-pair velocity correlation immersed in an unsteady isotropic homogeneous turbulent flow. Such correlation function is required to build reliable statistical models for inter-particle collisions, in the frame of the Euler–Lagrange approach, to be used in a broad range of two-phase flow applications. Computations of the turbulent flow have been carried out by means of Direct Numerical Simulation (DNS) by the Lattice Boltzmann Method (LBM). Moreover, the dependence of statistical properties of collisions on particle inertia and volumetric fraction is evaluated and quantified. It has been found that collision locations of particles of intermediate inertia, StK~1, occurs in regions where the fluid strain rate and dissipation are higher than the corresponding averaged values at particle positions. Connected with this fact, the average kinetic energy of colliding particles of intermediate inertia (i.e., Stokes number around 1) is lower than the value averaged over all particles. From the study of the particle-pair velocity correlation, it has been demonstrated that the colliding particle-pair velocity correlation function cannot be approximated by the Eulerian particle-pair correlation, obtained by theoretical approaches, as particle separation tends to zero, a fact related with the larger values of the relative radial velocity between colliding particles.
Highlights
Inter-particle collision of small particles immersed in a turbulent flow is a common micro-process found in both industrial and natural environments
As a result of the efforts to understand and quantify the enhancement of collision rates induced by inertia, two main mechanisms have been identified: on the one hand, preferential concentration, i.e., particle clustering, increases the probability for two particles to be at a colliding distance, and, on the other hand, detachment from fluid trajectories may enhance the relative velocity between two approaching particles
Some interesting results were found: as expected, inter-particle collision frequency augmented with increasing volume fraction and Stokes number, the Lagrangian integral time scale of particles decreased with volume fraction but increased with StK due to the decorrelation of particle motion induced by the increase in the number of collisions, the particle pair relative velocity at collision rose with growing StK but it decreased for higher values of αp, with this last effect being more pronounced for large inertia particles
Summary
Inter-particle collision of small particles immersed in a turbulent flow is a common micro-process found in both industrial and natural environments. Studied have been the particle–turbulent fluid interaction phenomena that lead to the formation of clusters in zones of low vorticity and high strain rate [25], favouring the occurrence of inter-particle collisions Such effect, described by the radial distribution function, and the relative velocity between particle pairs at contact point are the usual two elements employed for writing the collision kernel, defined usually as the collision frequency over the particle number density. The features of the resulting fractal set as well as its statistical characteristics depend on the nature of particle–fluid turbulence interaction and the particle Stokes number, StK (defined here as the quotient between the average particle response time and the Kolmogorov time scale of the flow) In this picture, the increase of relative velocity among neighbouring particles arises from the attractor folding in the velocity subspace, where the folded region boundaries are denominated caustics [27].
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