A unified Lagrangian trajectory model for particle diffusion in ducts

Abstract

A unified Lagrangian trajectory mapping approach to predict particle diffusion in ducts is presented, in which the effects of Brownian diffusion are accounted for using an effective particle radius concept. This approach is uniformly applicable to all particle sizes with the diffusion influence diminishing in importance as the physical particle size increases. The proposed model has been verified using bench-mark tests for cases of ultra fine particles when the physical particle size is negligible. Results predicted by this model agree very well with available analytical solutions for both uniform and parabolic flows within ducts of cylindrical and rectangular cross-sectional geometry over a wide range of the particle diffusivity. Using the concept of a particle diffusion sphere, it has been shown that the particle deposition efficiency due to diffusion in a conduit of regular polygon cross section is identical to the diffusion efficiency for a cylindrical tube having the same hydraulic radius.