Effect of Gravity on Particle Clustering and Collisions in Decaying Turbulence

Abstract

The preferential concentration of sedimenting particles in decaying homogeneous isotropic turbulence is investigated using radial distribution functions (RDF). Direct numerical simulations of polydisperse distributions of non-sedimenting and sedimenting particles of radii 10–55 μm are performed. We see a power law behaviour for the RDF in decaying turbulence and the power-law relation derived by Chun et al. (J Fluid Mech 536:219–251, 2005) for the RDF of non-sedimenting particles holds for sedimenting particles as well. Empirical formulas are generated for the power-law coefficients which are shown to be functions of the Stokes number and the Taylor Reynolds number for sedimenting particles. An in-depth analysis of the turbulent kinematic collision kernel for both non-sedimenting and sedimenting collision kernels confirms that gravity enhances the collision kernel for unequal sized particles and decreases for same-sized particles. Models are created for both monodisperse and bidisperse RDFs which are combined with existing models for the conditional radial relative velocities of colliding particles to predict kinematic collision kernels for both non-sedimenting and sedimenting particles. The effect on the collision kernel due to turbulence is also explored and enhancement of factors of up to three is observed with respect to the gravitational collision kernel.