The relative velocities and positions of monodisperse highinertia particle pairs in isotropic turbulence are studied using direct numerical simulations (DNS), as well as Langevin simulations (LS) based on a probability density function (PDF) kinetic model for pair relative motion. In a prior study (Rani et al. , J. Fluid Mech. , vol. 756, 2014, pp. 870–902), the authors developed a stochastic theory that involved deriving closures in the limit of high Stokes number for the diffusivity tensor in the PDF equation for monodisperse particle pairs. The diffusivity contained the time integral of the Eulerian twotime correlation of fluid relative velocities seen by pairs that are nearly stationary. The twotime correlation was analytically resolved through the approximation that the temporal change in the fluid relative velocities seen by a pair occurs principally due to the advection of smaller eddies past the pair by largescale eddies. Accordingly, two diffusivity expressions were obtained based on whether the pair centre of mass remained fixed during flow time scales, or moved in response to integralscale eddies. In the current study, a quantitative analysis of the (Rani et al. 2014) stochastic theory is performed through a comparison of the pair statistics obtained using LS with those from DNS.more »
Tutorial: Langevin Dynamics methods for aerosol particle trajectory simulations and collision rate constant modeling
The Langevin Dynamics (LD) method (also known in the literature as Brownian Dynamics) is routinely used to simulate aerosol particle trajectories for transport rate constant calculations as well as to understand aerosol particle transport in internal and external fluid flows. This tutorial intends to explain the methodological details of setting up a LD simulation of a population of aerosol particles and to deduce rate constants from an ensemble of classical trajectories. We discuss the applicability and limitations of the translational Langevin equation to model the combined stochastic and deterministic motion of particles in fields of force or fluid flow. The drag force and stochastic “diffusion” force terms that appear in the Langevin equation are discussed elaborately, along with a summary of common forces relevant to aerosol systems (electrostatic, gravity, van der Waals, …); a commonly used first order and a fourth order RungeKutta time stepping schemes for linear stochastic ordinary differential equations are presented. A MATLAB® implementation of a LD code for simulating particle settling under gravity using the first order scheme is included for illustration. Scaling analysis of aerosol transport processes and the selection of timestep and domain size for trajectory simulations are demonstrated through two specific aerosol processes: more »
 Award ID(s):
 1903432
 Publication Date:
 NSFPAR ID:
 10221107
 Journal Name:
 Journal of aerosol science
 Volume:
 155
 Issue:
 June
 Page Range or eLocationID:
 105746
 ISSN:
 00218502
 Sponsoring Org:
 National Science Foundation
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