The viscous flow over a thick permeable circular disk in the Reynolds number (Re) range of 10 to 130 and in the Darcy number (Da) range of 10−9 to 1 is examined. Direct numerical simulations are performed on a 2D grid with axisymmetric boundary conditions. Three flow regimes are observed: I, II, and III. In regime I (effectively impervious; ), the wake is characterized by the presence of a toroidal vortex whose length is approximately equal to that of an impervious disk. In regime II (transition; ), the increase in Da causes the vortex to shorten and move downstream and eventually vanishes at a critical Darcy number Dac. Regime III () is the highly permeable regime, in which there is no recirculation. In I, good agreement with existing experimental data for impervious disks is found. In III, an analytical expression for the drag force on the disk is derived, showing good agreement with the numerical results. A global upper limit of above which the disk is unable to maintain a recirculating wake for any Re is identified. Finally, in regime II, it is demonstrated that increasing the permeability can lead to large variations in the length of the recirculating wake but with minimal effect on the drag coefficient even when . This has important implications in our understanding of the locomotive strategies adopted by organisms that use porous bodies for movement.
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September 2017
Research Article|
September 18 2017
The effect of permeability on the flow past permeable disks at low Reynolds numbers
Cathal Cummins
;
Cathal Cummins
a)
1
Institute for Energy Systems, School of Engineering, University of Edinburgh
, EH9 3DW Edinburgh, United Kingdom
2
Institute of Molecular Plant Sciences, School of Biological Sciences, University of Edinburgh
, EH9 3BF Edinburgh, United Kingdom
3
SynthSys Centre for Systems and Synthetic Biology, School of Biological Sciences, University of Edinburgh
, EH9 3BF Edinburgh, United Kingdom
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Ignazio Maria Viola
;
Ignazio Maria Viola
b)
1
Institute for Energy Systems, School of Engineering, University of Edinburgh
, EH9 3DW Edinburgh, United Kingdom
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Enrico Mastropaolo;
Enrico Mastropaolo
4
Institute for Integrated Micro and Nano Systems, Scottish Microelectronics Centre, School of Engineering, University of Edinburgh
, EH9 3FF Edinburgh, United Kingdom
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Naomi Nakayama
Naomi Nakayama
2
Institute of Molecular Plant Sciences, School of Biological Sciences, University of Edinburgh
, EH9 3BF Edinburgh, United Kingdom
3
SynthSys Centre for Systems and Synthetic Biology, School of Biological Sciences, University of Edinburgh
, EH9 3BF Edinburgh, United Kingdom
5
Centre for Science at Extreme Conditions, School of Biological Sciences, University of Edinburgh
, EH9 3BF Edinburgh, United Kingdom
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a)
Electronic mail: Cathal.Cummins@ed.ac.uk
b)
Electronic mail: I.M.Viola@ed.ac.uk
Physics of Fluids 29, 097103 (2017)
Article history
Received:
April 18 2017
Accepted:
August 21 2017
Connected Content
A correction has been published:
Erratum: “The effect of permeability on the flow past permeable disks at low Reynolds numbers” [Phys. Fluids 29, 097103 (2017)]
Citation
Cathal Cummins, Ignazio Maria Viola, Enrico Mastropaolo, Naomi Nakayama; The effect of permeability on the flow past permeable disks at low Reynolds numbers. Physics of Fluids 1 September 2017; 29 (9): 097103. https://doi.org/10.1063/1.5001342
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