Bifurcations of a creeping air–water flow in a conical container

Adnan Balci, Morten Brøns, Miguel A. Herrada, Vladimir N. Shtern

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

This numerical study describes the eddy emergence and transformations in a slow steady axisymmetric air–water flow, driven by a rotating top disk in a vertical conical container. As water height (Formula presented.) and cone half-angle (Formula presented.) vary, numerous flow metamorphoses occur. They are investigated for (Formula presented.), and (Formula presented.). For small (Formula presented.), the air flow is multi-cellular with clockwise meridional circulation near the disk. The air flow becomes one cellular as (Formula presented.) exceeds a threshold depending on (Formula presented.). For all (Formula presented.), the water flow has an unbounded number of eddies whose size and strength diminish as the cone apex is approached. As the water level becomes close to the disk, the outmost water eddy with clockwise meridional circulation expands, reaches the interface, and induces a thin layer with anticlockwise circulation in the air. Then this layer expands and occupies the entire air domain. The physical reasons for the flow transformations are provided. The results are of fundamental interest and can be relevant for aerial bioreactors.
Original languageEnglish
JournalTheoretical and Computational Fluid Dynamics
Volume30
Issue number5
Pages (from-to)485-496
ISSN0935-4964
DOIs
Publication statusPublished - 2016

Keywords

  • Vortex breakdown
  • Rotating flow
  • Creeping flow
  • Bioreactors
  • Flow topology

Cite this

Balci, Adnan ; Brøns, Morten ; Herrada, Miguel A. ; Shtern, Vladimir N. / Bifurcations of a creeping air–water flow in a conical container. In: Theoretical and Computational Fluid Dynamics. 2016 ; Vol. 30, No. 5. pp. 485-496.
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abstract = "This numerical study describes the eddy emergence and transformations in a slow steady axisymmetric air–water flow, driven by a rotating top disk in a vertical conical container. As water height (Formula presented.) and cone half-angle (Formula presented.) vary, numerous flow metamorphoses occur. They are investigated for (Formula presented.), and (Formula presented.). For small (Formula presented.), the air flow is multi-cellular with clockwise meridional circulation near the disk. The air flow becomes one cellular as (Formula presented.) exceeds a threshold depending on (Formula presented.). For all (Formula presented.), the water flow has an unbounded number of eddies whose size and strength diminish as the cone apex is approached. As the water level becomes close to the disk, the outmost water eddy with clockwise meridional circulation expands, reaches the interface, and induces a thin layer with anticlockwise circulation in the air. Then this layer expands and occupies the entire air domain. The physical reasons for the flow transformations are provided. The results are of fundamental interest and can be relevant for aerial bioreactors.",
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Bifurcations of a creeping air–water flow in a conical container. / Balci, Adnan; Brøns, Morten; Herrada, Miguel A.; Shtern, Vladimir N.

In: Theoretical and Computational Fluid Dynamics, Vol. 30, No. 5, 2016, p. 485-496.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Bifurcations of a creeping air–water flow in a conical container

AU - Balci, Adnan

AU - Brøns, Morten

AU - Herrada, Miguel A.

AU - Shtern, Vladimir N.

PY - 2016

Y1 - 2016

N2 - This numerical study describes the eddy emergence and transformations in a slow steady axisymmetric air–water flow, driven by a rotating top disk in a vertical conical container. As water height (Formula presented.) and cone half-angle (Formula presented.) vary, numerous flow metamorphoses occur. They are investigated for (Formula presented.), and (Formula presented.). For small (Formula presented.), the air flow is multi-cellular with clockwise meridional circulation near the disk. The air flow becomes one cellular as (Formula presented.) exceeds a threshold depending on (Formula presented.). For all (Formula presented.), the water flow has an unbounded number of eddies whose size and strength diminish as the cone apex is approached. As the water level becomes close to the disk, the outmost water eddy with clockwise meridional circulation expands, reaches the interface, and induces a thin layer with anticlockwise circulation in the air. Then this layer expands and occupies the entire air domain. The physical reasons for the flow transformations are provided. The results are of fundamental interest and can be relevant for aerial bioreactors.

AB - This numerical study describes the eddy emergence and transformations in a slow steady axisymmetric air–water flow, driven by a rotating top disk in a vertical conical container. As water height (Formula presented.) and cone half-angle (Formula presented.) vary, numerous flow metamorphoses occur. They are investigated for (Formula presented.), and (Formula presented.). For small (Formula presented.), the air flow is multi-cellular with clockwise meridional circulation near the disk. The air flow becomes one cellular as (Formula presented.) exceeds a threshold depending on (Formula presented.). For all (Formula presented.), the water flow has an unbounded number of eddies whose size and strength diminish as the cone apex is approached. As the water level becomes close to the disk, the outmost water eddy with clockwise meridional circulation expands, reaches the interface, and induces a thin layer with anticlockwise circulation in the air. Then this layer expands and occupies the entire air domain. The physical reasons for the flow transformations are provided. The results are of fundamental interest and can be relevant for aerial bioreactors.

KW - Vortex breakdown

KW - Rotating flow

KW - Creeping flow

KW - Bioreactors

KW - Flow topology

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DO - 10.1007/s00162-016-0391-z

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