Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-19T14:07:09.879Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow instabilities between two parallel planes semi-obstructed by an easily penetrable porous medium

Published online by Cambridge University Press:  17 November 2011

N. Silin ,
J. Converti ,
D. Dalponte  and
A. Clausse
N. Silin
Affiliation:
CONICET-CNEA and Instituto Balseiro, 8400 Bariloche, Argentina
J. Converti
Affiliation:
CONICET-CNEA and Instituto Balseiro, 8400 Bariloche, Argentina
D. Dalponte
Affiliation:
CNEA-CONICET and Universidad Nacional del Centro, 7000 Tandil, Argentina
A. Clausse*
Affiliation:
CNEA-CONICET and Universidad Nacional del Centro, 7000 Tandil, Argentina
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A study of instabilities in planar flows produced by the presence of a parallel penetrable porous obstruction is presented. The case considered is a flow between parallel plates partially obstructed by a porous medium. The most unstable perturbation modes are obtained solving numerically the eigenvalue problem derived from the linear stability analysis of the two-dimensional Navier–Stokes equations applied to the geometry of interest. The analysis leads to an extended Orr–Sommerfeld equation including a porous term. It was found that the ratios of the permeability and depth of the obstruction with respect to the free flow layer depth are the relevant parameters influencing the stability margin and the structure of the most unstable modes. To validate the conclusions of the theoretical analysis, an experiment with air flowing through a channel semi-obstructed by a regular array of cylindrical wires was performed. The critical Reynolds number, which was determined by measuring the amplitude of velocity fluctuations at the interface of the porous medium, agrees with the theoretical predictions. The dominant instability mode was characterized by the cross-section profile of the root mean square of the velocity perturbations, which matches reasonable well with the eigenfunction of the most unstable eigenvalue. Also, the wavenumber was determined by correlating the velocity measurements in two sequential locations along the channel, which compares well with the theoretical value.

JFM classification

Boundary Layers: Boundary layer structure Instability: Instability Low-Reynolds-number flows: Low-Reynolds-number flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 689 , 25 December 2011 , pp. 417 - 433
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Beavers, G. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207.CrossRefGoogle Scholar
2. Bousmar, D., Rivière, P. N., Paquier, A., MoreL, R. & Zech, Y. 2005 Upstream discharge distribution in compound-channel flumes. J. Hydraul. Engng 131, 408–412.CrossRefGoogle Scholar
3. Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 35–72.CrossRefGoogle Scholar
4. Bruun, H. H. 1995 Hot Wire Anemometry: Principles and Signal Analysis. Oxford University.CrossRefGoogle Scholar
5. Chew, Y. T., Khoo, B. C. & Li, G. L. 1998 An investigation of wall effects on hot-wire measurements using a bent sublayer probe. Meas. Sci. Technol. 9, 67–85.CrossRefGoogle Scholar
6. Finnigan, J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519–571.CrossRefGoogle Scholar
7. Gayev, Y. A. & Hunt, J. C. R. 2007 Flow and Transport Processes with Complex Obstructions, Series II: Mathematics, Physics and Chemistry , 236. Springer.CrossRefGoogle Scholar
8. Ghisalberti, M. 2009 Obstructed shear flows: similarities across systems and scales. J. Fluid Mech. 641, 51–61.CrossRefGoogle Scholar
9. Hill, A. A. & Straughan, B. 2008 Poiseuille flow in a fluid overlying a porous medium. J. Fluid Mech. 603, 137–149.CrossRefGoogle Scholar
10. Kao, T. W. & Park, C. 1970 Experimental investigations of the stability of channel flows. Part 1. Flow of a single liquid in a rectangular channel. J. Fluid Mech. 43, 145–164.CrossRefGoogle Scholar
11. Larson, R. E. & Higdon, J. J. L. 1986 Microscopic flow near the surface of two-dimensional porous media. Part l. Axial flow. J . Fluid Mech. 166, 444–472.CrossRefGoogle Scholar
12. Larson, R. E. & Higdon, J. L. 1987 Microscopic flow near the surface of two-dimensional porous media. Part 2. Transverse flow. J. Fluid Mech. 178, 119–136.CrossRefGoogle Scholar
13. Lexmond, A. S., Mudde, R. F. & Van der hagen, T. H. 2005 Visualisation of the vortex street and characterisation of the cross flow in the gap between two sub-channels, Eleventh Int. Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11), Avignon, France, 2–6 October, Paper 122.Google Scholar
14. López, F. & García, M. H. 2001 Mean flow and turbulence structure of open-channel flow through non-emergent vegetation. J. Hydraul. Engng 127, 392–402.CrossRefGoogle Scholar
15. Mathieu, J. & Scott, J. 2000 An Introduction to Turbulent Flow, p. 17. Cambridge University Press.CrossRefGoogle Scholar
16. Merzari, E., Wang, S., Ninokata, H. & Theofilis, V. 2008 Biglobal linear stability analysis for the flow in eccentric annular channels and a related geometry. Phys. Fluids 20, 114104.CrossRefGoogle Scholar
17. Meyer, L. 2010 From discovery to recognition of periodic large scale vortices in rod bundles as source of natural mixing between subchannels – A review. Nucl. Engng Des. 240, 1575–1588.CrossRefGoogle Scholar
18. Meyer, L. & Rehme, K. 1995 Periodic vortices in flow through channels with longitudinal slots or fins. Proceedings of the Tenth Symposium on Turbulent Shear Flows, University Park, PA, 14–16 August, vol. 2, S.P2/55–P2/60.Google Scholar
19. Poggi, D. & Katul, G. G. 2008 Micro and macro dispersive fluxes in canopy flows. Acta Geophys. 56, 778–800.CrossRefGoogle Scholar
20. Raupach, M. R., Finnigan, J. J. & Brunet, Y. 1996 Coherent eddies and turbulence in vegetation canopies: the mixing-layer analogy. Boundary-Layer Meteorol. 78, 351–382.CrossRefGoogle Scholar
21. Schlichting, H. & Gersten, K. 2000 Boundary-Layer Theory. McGraw Hill, 1979.CrossRefGoogle Scholar
22. Socolofsky, S. A. & Jirka, G. H. 2004 Large-scale flow structures and stability in shallow flows. J. Environ. Engng Sci. 3, 451–462.CrossRefGoogle Scholar
23. Weideman, J. A. C. & Reddy, S. C. 2000 A MATLAB differentiation matrix suite. ACM Trans. Math. Softw. 26, 465–519.CrossRefGoogle Scholar
24. White, B. L. & Nepf, H. M. 2007 Shear instability and coherent structures in shallow flow adjacent to a porous layer. J. Fluid Mech. 593, 1–32.CrossRefGoogle Scholar
25. Yue, Z. & Malmstrom, T. G. 1998 A simple method for low-speed hot-wire anemometer calibration. Meas. Sci. Technol. 9, 1506.CrossRefGoogle Scholar