Analysis of the advection–diffusion mixing by the mapping method formalism in 3D open‐flow devices

Abstract

This article extends the analysis of laminar mixing driven by a chaotic flow in the presence of diffusion to three-dimensional open-flow devices by means of the mapping-matrix method. The extended formulation of the mapping matrix recently proposed by Gorodetskyi et al. (2012) allows inclusion of the molecular diffusion in the mixing process. This provides an efficient numerical tool for understanding the interplay between a chaotic advective field and diffusion, especially for high Péclet numbers. As a prototypical open-flow device we consider the partitioned-pipe mixer. Results deriving from the application of the extended mapping method are compared with Galerkin simulations, and a close agreement is found. Short-term properties in the evolution of the concentration and the effect of axial diffusion are also addressed. © 2013 American Institute of Chemical Engineers

Scalar transport in inline mixers with spatially periodic flows

“…In the past few decades, the fundamentals and applications of mass/scalar transport in spatially periodic laminar flows have been studied in numerous theoretical and numerical investigations. [5][6][7][8][9][10][11][12] Nevertheless, a complete understanding is not achieved yet. Particularly, experimental studies are limited, i.e., restricted to highly idealized flow geometries or allowing only partial access to the flow domain with (optical) diagnostic tools.…”

Experimental and computational study of scalar modes in a periodic laminar flow

“…The longer-term dye patterns thus still have a physical meaning by in fact visualizing the finite-Pe dominant eigenmode for very high (yet finite) Pe. A similar case is studied by Gorodetskyi et al [16], where numerical diffusion is exploited to emulate diffusion at extreme Pe. The dominant mode of the finite-Pe case at more moderate Pe can therefore be seen as a smeared-out version of the infinite-Pe case.…”

“…(6)) from data at discrete time levels. It assumes that the subsequent time levels relate via a mapping: c nþ1 ¼ Ac n (16) where c n denotes the scalar field in discrete partitions in the domain at time level t n ¼ nDt and A is a linear operator that maps a scalar field c n to the consecutive one c nþ1 . The eigenfunctioneeigenvalue pairs of the mapping matrix A are the approximations for the eigenfunctioneeigenvalue pairs {4 k ,m k } of the advectionediffusion operator L 2 .…”

“…9) determine the asymptotic mixing pattern corresponding with an eigenmode of period-1 which is non-decaying, i.e. m 0 ¼ 0 [16]. The scalar field exponentially converges on this pattern independently of the initial distribution.…”

Analysis of Advective–Diffusive Transport in Complex Mixing Devices by the Diffusive Mapping Method

“…The conventional mapping method is restricted to purely advective transport. However, a recent extension of the method enables incorporation of diffusion as well . This expands the area of application tremendously.…”