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Characterization of stationary mixing patterns in a three-dimensional open Stokes flow : Spectral properties, localization and mixing regimes

Giona, M.; Cerbelli, S. and Garofalo, F. LU (2009) In Journal of Fluid Mechanics 639. p.291-341
Abstract

This article analyses stationary scalar mixing downstream an open flow Couette device operating in the creeping flow regime. The device consists of two coaxial cylinders of finite length Lz, and radii κR and R (<1), which can rotate independently. At relatively large values of the aspect ratioα = Lz/R 1, and of the Pclet number Pe, the stationary response of the system can be accurately described by enforcing the simplifying assumption of negligible axial diffusion. With this approximation, homogenization along the device axis can be described by a family of generalized one-dimensional eigenvalue problems with the radial coordinate as independent variable. A variety of mixing regimes can be observed by varying... (More)

This article analyses stationary scalar mixing downstream an open flow Couette device operating in the creeping flow regime. The device consists of two coaxial cylinders of finite length Lz, and radii κR and R (<1), which can rotate independently. At relatively large values of the aspect ratioα = Lz/R 1, and of the Pclet number Pe, the stationary response of the system can be accurately described by enforcing the simplifying assumption of negligible axial diffusion. With this approximation, homogenization along the device axis can be described by a family of generalized one-dimensional eigenvalue problems with the radial coordinate as independent variable. A variety of mixing regimes can be observed by varying the geometric and operating parameters. These regimes are characterized by different localization properties of the eigenfunctions and by different scaling laws of the real part of the eigenvalues with the Pclet number. The analysis of this model flow reveals the occurrence of sharp transitions between mixing regimes, e.g. controlled by the geometric parameter. The eigenvalue scalings can be theoretically predicted by enforcing eigenfunction localization and simple functional equalities relating the behaviour of the eigenvalues to the functional form of the associated eigenfunctions. Several flow protocols corresponding to different geometric and operating conditions are considered. Among these protocols, the case where the inner and the outer cylinders counter-rotate exhibits a peculiar intermediate scaling regime where the real part of the dominant eigenvalue is independent of Pe over more than two decades of Pe. This case is thoroughly analysed by means of scaling analysis. The practical relevance of the results deriving from spectral analysis for fluid mixing problems in finite-length Couette devices is addressed in detail. © 2009 Cambridge University Press.

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author
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Fluid Mechanics
volume
639
pages
51 pages
publisher
Cambridge University Press
external identifiers
  • scopus:76349093389
ISSN
0022-1120
DOI
10.1017/S0022112009991066
language
English
LU publication?
no
id
2c15f4a0-c2b6-42ff-9e88-12f5f5b1cb45
date added to LUP
2016-06-27 10:10:29
date last changed
2017-01-01 08:29:08
@article{2c15f4a0-c2b6-42ff-9e88-12f5f5b1cb45,
  abstract     = {<p>This article analyses stationary scalar mixing downstream an open flow Couette device operating in the creeping flow regime. The device consists of two coaxial cylinders of finite length L<sub>z</sub>, and radii κR and R (&lt;1), which can rotate independently. At relatively large values of the aspect ratioα = L<sub>z</sub>/R 1, and of the Pclet number Pe, the stationary response of the system can be accurately described by enforcing the simplifying assumption of negligible axial diffusion. With this approximation, homogenization along the device axis can be described by a family of generalized one-dimensional eigenvalue problems with the radial coordinate as independent variable. A variety of mixing regimes can be observed by varying the geometric and operating parameters. These regimes are characterized by different localization properties of the eigenfunctions and by different scaling laws of the real part of the eigenvalues with the Pclet number. The analysis of this model flow reveals the occurrence of sharp transitions between mixing regimes, e.g. controlled by the geometric parameter. The eigenvalue scalings can be theoretically predicted by enforcing eigenfunction localization and simple functional equalities relating the behaviour of the eigenvalues to the functional form of the associated eigenfunctions. Several flow protocols corresponding to different geometric and operating conditions are considered. Among these protocols, the case where the inner and the outer cylinders counter-rotate exhibits a peculiar intermediate scaling regime where the real part of the dominant eigenvalue is independent of Pe over more than two decades of Pe. This case is thoroughly analysed by means of scaling analysis. The practical relevance of the results deriving from spectral analysis for fluid mixing problems in finite-length Couette devices is addressed in detail. © 2009 Cambridge University Press.</p>},
  author       = {Giona, M. and Cerbelli, S. and Garofalo, F.},
  issn         = {0022-1120},
  language     = {eng},
  pages        = {291--341},
  publisher    = {Cambridge University Press},
  series       = {Journal of Fluid Mechanics},
  title        = {Characterization of stationary mixing patterns in a three-dimensional open Stokes flow : Spectral properties, localization and mixing regimes},
  url          = {http://dx.doi.org/10.1017/S0022112009991066},
  volume       = {639},
  year         = {2009},
}