Direct numerical simulation of a coagulating aerosol in a two-dimensional, incompressible, iso-thermal shear layer is performed. The evolution of the particle field is obtained by utilizing a nodal model to approximate the aerosol general dynamic equation (GDE). The GDE is written in discrete form as a population balance on each particle size and describes particle dynamics under the influence of various physical phenomena: convection, diffusion, and coagulation. The nodal approach is advantageous in that there are no a priori assumptions regarding the nature of the particle size distribution and therefore does not suffer from the severe constraints of other methodologies. This approach divides the particle size distribution into "bins," for each of which a transport equation is obtained. A coagulation Damköhler number is defined to represent the ratio of the convective time scale to the coagulation time scale. Simulations are performed at a Reynolds number of 200 and coagulation Damköhler numbers of 1 and 10. The nanoparticle field is presented as a function of space, time and size. Results indicate that strong spatial variations in the particle concentrations develop in time and that these spatial gradients act to increase the geometric standard deviation of the particle size distribution. As the coagulation Damköhler number is increased, particle growth increases and particle size distributions wider than the self-preserving limit are predicted. The capture of the evolution of the particle field as a function of space, time and size suggests that the methodology is sufficiently general and robust to be useful in predicting the growth and dynamics in inhomogeneous, and possibly, turbulent flows.
Bibliographical noteFunding Information:
The first author acknowledges the support of the National Science Foundation under Grant ACI-9982274. Computational resources are provided by the Minnesota Supercomputing Institute.
Copyright 2019 Elsevier B.V., All rights reserved.
- Direct numerical simulation
- Mixing layers
- Navier-Stokes equations
- Nodal methods