Characterization of stationary mixing patterns in a threedimensional open Stokes flow : Spectral properties, localization and mixing regimes
(2009) In Journal of Fluid Mechanics 639. p.291341 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 L_{z}, and radii κR and R (<1), which can rotate independently. At relatively large values of the aspect ratioα = L_{z}/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 onedimensional 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 L_{z}, and radii κR and R (<1), which can rotate independently. At relatively large values of the aspect ratioα = L_{z}/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 onedimensional 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 counterrotate 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 finitelength Couette devices is addressed in detail. © 2009 Cambridge University Press.
(Less)
 author
 Giona, M.; Cerbelli, S. and Garofalo, F. ^{LU}
 publishing date
 200911
 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
 00221120
 DOI
 10.1017/S0022112009991066
 language
 English
 LU publication?
 no
 id
 2c15f4a0c2b642ff9e8812f5f5b1cb45
 date added to LUP
 20160627 10:10:29
 date last changed
 20160715 14:10:21
@misc{2c15f4a0c2b642ff9e8812f5f5b1cb45, 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 (<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 onedimensional 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 counterrotate 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 finitelength Couette devices is addressed in detail. © 2009 Cambridge University Press.</p>}, author = {Giona, M. and Cerbelli, S. and Garofalo, F.}, issn = {00221120}, language = {eng}, pages = {291341}, publisher = {ARRAY(0x6ecff58)}, series = {Journal of Fluid Mechanics}, title = {Characterization of stationary mixing patterns in a threedimensional open Stokes flow : Spectral properties, localization and mixing regimes}, url = {http://dx.doi.org/10.1017/S0022112009991066}, volume = {639}, year = {2009}, }