Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-28T20:13:49.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional flow in circular cavities of large spanwise aspect ratio

Published online by Cambridge University Press:  30 July 2012

Owen Tutty ,
Ralph Savelsberg  and
Ian P. Castro
Ralph Savelsberg
Affiliation:
Engineering and the Environment, University of Southampton, Highfield, Southampton SO17 1BJ, UK
Ian P. Castro*
Affiliation:
Engineering and the Environment, University of Southampton, Highfield, Southampton SO17 1BJ, UK
*
†Email address for correspondence: i.castro@soton.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Experimental data are presented for the vortex flow in a nominally two-dimensional circular cavity. The vortex is driven by a separated shear layer along an open section of the cavity circumference. It is shown that the core vortex flow is perturbed three-dimensionally. An inviscid analysis of an ideal core (solid body) vortex is given and it is shown that this flow contains a steady perturbation whose characteristics are almost exactly those identified in the experiments. Viscous effects reduce (by a few per cent) the spanwise wavelength of the perturbation and also lead, via spatial variations in Reynolds stress, to a modification of the core flow so that the radial profile of the circumferential velocity is ‘S’-shaped, rather than linear.

JFM classification

Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 707 , 25 September 2012 , pp. 551 - 574
Copyright
Copyright © Cambridge University Press 2012

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.)

Footnotes

‡

Present address: Faculty of Military Sciences, Netherlands Defence Academy, PO Box 10000, 1780 CA Den Helder, The Netherlands.

References

1. Albensoeder, S. & Kuhlmann, H. C. 2006 Nonlinear three-dimensional flow in the lid-driven square cavity. J. Fluid Mech. 569, 465–480.CrossRefGoogle Scholar
2. Albensoeder, S., Kuhlmann, H. C. & Rath, H. J. 2001 Three-dimensional centrifugal-flow instabilities in the lid-driven-cavity problem. Phys. Fluids 13, 121–135.CrossRefGoogle Scholar
3. Barkley, D., Gomes, M. G. M. & Henderson, R. D. 2002 Three-dimensional instability in flow over a backward facing step. J. Fluid Mech. 473, 167–190.CrossRefGoogle Scholar
4. Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.Google Scholar
5. Bayly, B. J. 2001 Three-dimensional centrifugal-type instabilities in inviscid two-dimensional flows. Phys. Fluids 13, 56–64.Google Scholar
6. Billant, P. & Gallaire, F. 2005 Generalized Rayleigh criterion for non-axisymmetric centrifugal instabilities. J. Fluid Mech. 542, 365–379.CrossRefGoogle Scholar
7. Brès, G. A. & Colonius, T. 2008 Three-dimensional instabilities in compressible flow over open cavities. J. Fluid Mech. 599, 309–339.CrossRefGoogle Scholar
8. Chernyshenko, S. 2009 VortexCell2050: fundamentals of actively controlled flows with trapped vortices. EU Executive Summary report for contract no. AST4-CT-2005-012139 012139,http://cordis.europa.eu/documents/documentlibrary/120142501EN6.pdf.Google Scholar
9. Colonius, T. 2001 An overview of simulation, modelling and active control of flow/acoustic resonance in open cavities. AIAA Paper 2001-0076.Google Scholar
10. Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
11. Faure, T. M., Adrianos, P., Lusseyran, F. & Pastur, L. 2007 Visualisations of the flow inside an open cavity at medium range Reynolds numbers. Exp. Fluids 42, 169–184.CrossRefGoogle Scholar
12. Faure, T. M., Pastur, L., Lusseyran, F., Fraigneau, Y. & Bisch, D. 2009 Three-dimensional centrifugal instabilities development inside a parallelepipedic open cavity of various shape. Exp. Fluids 47, 395–410.CrossRefGoogle Scholar
13. Gharib, M. & Roshko, A. 1987 The effect of flow oscillations on cavity drag. J. Fluid Mech. 177, 501–530.CrossRefGoogle Scholar
14. Hetsch, T., Savelsberg, R., Chernyshenko, S. & Castro, I. P. 2009 Fast numerical evaluation of flow fields with vortex cells. Eur. J. Mech. B/Fluids 28, 660–669.CrossRefGoogle Scholar
15. Kelvin, Lord 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155–168.Google Scholar
16. Komerath, N. M., Ahuja, K. K. & Chambers, F. W. 1987 Prediction and measurement of flows over cavities – a survey. AIAA Paper 87-0166.CrossRefGoogle Scholar
17. Leriche, E. & Gavrilakis, S. 2000 Direct numerical simulation of the flow in a lid-driven cubical cavity. Phys. Fluids 12, 1363–1376.CrossRefGoogle Scholar
18. Lessen, M., Deshpande, N. V. & Hadji-Ohanes, B. 1973 Stability of a potential vortex with a non-rotating and rigid-body rotating top-hat jet core. J. Fluid Mech. 60, 459–460.CrossRefGoogle Scholar
19. Maull, D. J. & East, L. F. 1963 Three-dimensional flow in cavities. J. Fluid Mech. 16, 620–632.CrossRefGoogle Scholar
20. Olsman, W. F. J. & Colonius, T. 2011 Numerical simulation of flow over an aerofoil with a cavity. AIAA J. 51, 143–149.CrossRefGoogle Scholar
21. Olsman, W. F. J., Willems, J. F. H., Hirschberg, A., Colonius, T. & Trieling, R. R. 2011 Flow around a NACA0018 aerofoil with a cavity and its dynamical reponse to acoustic forcing. Exp. Fluids 51, 493–509.CrossRefGoogle Scholar
22. Prasad, A. K. & Koseff, J. R. 1989 Reynolds number and end wall effects on a lid-driven cavity. Phys. Fluids A 1, 208.CrossRefGoogle Scholar
23. Rockwell, D. & Naudasher, E. 1978 Review – self sustaining oscillations of flow past cavities. Trans. ASME: J. Fluids Engng 100, 152–165.Google Scholar
24. Rossiter, J. E. 1964 Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Tech. Rep. 3438. ARC.Google Scholar
25. Rowley, C. W., Colonius, T. & Basu, A. J. 2002 On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities. J. Fluid Mech. 455, 315–346.CrossRefGoogle Scholar
26. Rowley, C. W. & Williams, D. R. 2006 Dynamics and control of high-Reynolds-number flow over open cavities. Annu. Rev. Fluid Mech. 38, 251–276.CrossRefGoogle Scholar
27. Savelsberg, R. & Castro, I. P. 2009 Vortex flows in open cylindrical-section cavities. Exp. Fluids 46, 485–497.CrossRefGoogle Scholar
28. Savelsberg, R., Obermeier, E., Schiffer, M. & Castro, I. P. 2012 Calibration and use of a surface fence for wall shear stress measurements in turbulent flows. Exp. Fluids, doi:10.1007/s00348-012-1304-6.CrossRefGoogle Scholar
29. Shankar, P. N. & Deshpande, M. D. 2000 Fluid mechanics in the driven cavity. Annu. Rev. Fluid Mech. 32, 93–136.CrossRefGoogle Scholar
30. Theofilis, V., Duck, P. W. & Owen, J. 2004 Viscous linear stability analysis of rectangular duct and cavity flows. J. Fluid Mech. 505, 249–286.CrossRefGoogle Scholar
31. Williams, P. T. & Baker, A. J. 1997 Numerical simulations of laminar flow over a three-dimensional backward-facing step. Intl J. Numer. Meth. Fluids 24, 1159–1183.3.0.CO;2-R>CrossRefGoogle Scholar