Article,
Population Balance Equation for Turbulent Polydispersed Inertial Droplets and Particles
Journal of Fluid Mechanics, (Oct 17, 2017)
DOI: 10.1017/jfm.2017.653
Abstract
This paper presents a probability density function (PDF) form of the population
balance equation (PBE) for polysized and polyshaped droplets and solid particles in
turbulent flows. A key contribution of this paper lies in the inclusion of an explicit
consideration of the inertial effects and the shape of particles in the PDF-PBE
formulation. The number density is taken as a function of droplet or particle size
(volume) and shape as well as space and time. Potentially, other particle properties
could also be included in the formulation. Inertial effects are quantified through the
Stokes number, leading to accurate modelling of the different trajectories that are
followed by droplets and/or particles with different sizes and shapes. To treat these
effects, a new affordable approach is proposed and referred to as the method of
Stokes binning. Here, the inertial dispersed elements are accelerated due to fluid
dynamic forces associated with an averaged Stokes number in each bin. The model
is validated against two data sets. The first data set includes a series of numerical
test cases involving the injection of polyshaped droplets ranging in size from 1 to 50
μm into a turbulent jet resulting in inlet Stokes numbers ranging from 0.03 to 75.2.
The second data set consists of an experimental case focusing on the dispersion of
60 and 90 μm spherical droplets in a turbulent round jet, resulting in inlet Stokes
numbers of 53 and 122, respectively. The results confirm the ability of the approach
to accurately model the polysized and polyshaped droplet dispersion using as few as
eight Stokes bins. This approach has the potential to greatly reduce the computational
cost of modelling the evolution of inertial droplets and particles in turbulent flows.
