Hostname: page-component-7dd5485656-bvgqh Total loading time: 0 Render date: 2025-10-31T01:12:19.782Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear instability analysis of low- $Re$ incompressible flow over a long rectangular finite-span open cavity

Published online by Cambridge University Press:  21 June 2016

Qiong Liu ,
Francisco Gómez Open the ORCID record for Francisco Gómez [Opens in a new window]  and
Vassilios Theofilis
Qiong Liu
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, Madrid, Spain
Francisco Gómez
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, Victoria 3800, Australia
Vassilios Theofilis*
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, Madrid, Spain School of Engineering, University of Liverpool, Browlow Hill, Liverpool L69 3GH, UK
*
†Email address for correspondence: vassilis@aero.upm.es
Get access Rights & Permissions [Opens in a new window]

Abstract

TriGlobal linear instability analysis and direct numerical simulations have been performed to unravel the mechanisms ultimately responsible for transition of steady laminar flow over a long rectangular finite-span open cavity with dimensions $L$  :  $D$  :  $W$ $=$ 6 : 1 : 2 to unsteadiness. The steady laminar three-dimensional flow loses stability at $\mathit{Re}_{D,cr}\approx 1080$ as a consequence of linear amplification of a travelling eigenmode that is qualitatively analogous to the shear-layer mode known from analyses of flow in spanwise-periodic cavities, but has a three-dimensional structure which is strongly influenced by the cavity lateral walls. Differences in the eigenspectrum of the present and the spanwise homogeneous flow configuration are documented. Topological changes exerted on the steady laminar flow by linear amplification of the unstable shear-layer mode are reminiscent of observations in experiments at an order of magnitude higher Reynolds number.

JFM classification

Instability: Instability Instability: Transition to turbulence

Information

Type
Rapids
Information
Journal of Fluid Mechanics , Volume 799 , 25 July 2016 , R2
Check for updates
Copyright
© 2016 Cambridge University Press 

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.)

Article purchase

Temporarily unavailable

References

Åkervik, E., Brandt, L., Henningson, D. S. & Hœpffner, J. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18, 068102,1–4.Google Scholar
Alvarez, J., Kerschen, E. J. & Tumin, A.2004 A theoretical model for cavity acoustic resonance in subsonic flow. AIAA Paper 2004-2845.Google Scholar
Ashcroft, G. & Zhang, X. 2005 Vortical structures over rectangular cavities at low speed. Phys. Fluids 17, 015104,1–8.CrossRefGoogle Scholar
Barkley, D., Gomez, M. G. & Henderson, R. D. 2002 Three-dimensional instability in flow over a backward-facing step. J. Fluid Mech. 473, 167–190.Google Scholar
Brés, G. A. & Colonius, T. 2008 Three dimensional instabilities in compressible flow over open cavity. J. Fluid Mech. 599, 309–339.Google Scholar
Cattafesta, L. N. & Sheplak, M. 2011 Actuators for active flow control. Annu. Rev. Fluid Mech. 43, 247–272.CrossRefGoogle Scholar
Cattafesta, L. N., Song, Q., William, D. R., Rowley, C. W. & Alvi, F. S. 2008 Active control of flow-induced cavity oscillations. Prog. Aerosp. Sci. 44, 479–502.Google Scholar
Citro, V. F. G., Brandt, L. & Luchini, P. 2015 Linear three-dimensional global and asymptotic stability analysis of incompressible open cavity flow. J. Fluid Mech. 768, 113–140.Google Scholar
Crook, S., Kelso, R. & Drobik, J. 2007 Aeroacoustics of aircraft cavities. In 16th Australasian Fluid Mechanics Conference (AFMC) (ed. Jacobs, P., Mclntyre, T. & Cleary, M.), pp. 429–435. School of Engineering, The University of Queensland.Google Scholar
Crook, S. D., Lau, T. C. W. & Kelso, R. M. 2013 Three-dimensional flow within shallow, narrow cavities. J. Fluid Mech. 735, 587–612.CrossRefGoogle Scholar
Délery, J. 2013 Three-Dimensional Separated Flow Topology. Wiley.Google Scholar
De Vicente, J., Basley, J., Meseguer, F., Soria, J. & Theofilis, V. 2014 Three dimensional instabilities over a rectangular open cavity: from linear stability analysis to experimentation. J. Fluid Mech. 748, 189–220.Google Scholar
Douay, C. L., Pastur, L. R. & Lusseyran, F. 2016 Centrifugal instabilities in an experimental open cavity flow. J. Fluid Mech. 788, 670–694.CrossRefGoogle Scholar
Faure, T. M., Adrianos, P., Lusseyran, F. & Pastur, L. 2007 Visualizations of the flow inside an open cavity at medium range Reynolds numbers. Exp. Fluids 42, 169–184.Google Scholar
Faure, T. M., Pastur, L. R., Lusseyran, F., Fraigneau, Y. & Bisch, D. 2009 Three-dimensional centrifugal instabilities development inside a parallelepipedic open cavity of various shapes. Exp. Fluids 47 (3), 395–410.CrossRefGoogle Scholar
Fischer, P. F. & Ronquist, E. M. 1994 Spectral element methods for large scale parallel Navier–Stokes calculations. Comput. Meth. Appl. Mech. Engng 116, 69–76.Google Scholar
Forestier, N., Jacquin, L. & Geffroy, P. 2003 The mixing layer over a deep cavity at high-subsonic speed. J. Fluid Mech. 475, 101–145.Google Scholar
George, B., Ukeiley, L., Cattafesta, L. N. & Taira, K.2015 Control of three-dimensional cavity flow using leading-edge solt slowing. AIAA Paper 2015-1059.Google Scholar
Gharib, M. & Roshko, A. 1987 The effect of flow oscillations on cavity drag. J. Fluid Mech. 177, 501–530.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.Google Scholar
Krishnamurty, K.1955 Acoustic radiation from two dimensional rectangular coutouts in aerodynamic surfaces. NACA TN 3487.Google Scholar
Larchevêque, L., Sagaut, P. & Labbé, O. 2007 Large-eddy simulation of a subsonic cavity flow including asymmetric three-dimensional effects. J. Fluid Mech. 577, 105–126.CrossRefGoogle Scholar
Larchevêque, L., Sagaut, P., Lê, T. H. & Comte, P. 2004 Large-eddy simulation of compressible flow in a three-dimensional open cavity at high Reynolds number. J. Fluid Mech. 516, 265–301.Google Scholar
Le Clainche, S., Li, J. I., Theofilis, V. & Soria, J. 2015 Flow around a hemisphere-cylinder at high angle of attack and low Reynolds number. Aerosp. Sci. Technol. 44, 77–87.CrossRefGoogle Scholar
Liu, Q.2016 Global instability analysis and control of three-dimensional long open cavity flow. PhD thesis, Universidad Politécnica de Madrid.Google Scholar
Liu, Q., Gómez, F. & Theofilis, V. 2015 Linear instability analysis of incompressible flow over a cuboid cavity. In Procedia IUTAM, vol. 14, pp. 511–518. IUTAM-ABCM Symposium on Laminar Turbulent Transition. Elsevier.Google Scholar
Meseguer, F., de Vicente, J., Valero, E. & Theofilis, V. 2014 On linear instability mechanisms in incompressible open cavity flow. J. Fluid Mech. 752, 219–236.CrossRefGoogle Scholar
Nayyar, P., Barakos, G. N. & Badcock, K. J. 2007 Numerical study of transonic cavity flows using large-eddy and detached-eddy simulation. Aeronaut. J. 111 (1117), 153–164.CrossRefGoogle Scholar
Özsoy, E., Rambaud, P., Stitou, A. & Riethmuller, M. L. 2005 Vortex characteristics in laminar cavity flow at very low Mach number. Exp. Fluids 38, 133–145.Google Scholar
Peplinski, A., Schlatter, P., Fischer, P. F. & Henningson, D. S. 2014 Stability tools for the spectral-element code nek5000: application to jet-in crossflow. In Spectral and High Order Methods for Partial Differential Equations – ICOSAHOM 2012, Lecture Notes in Computational Science and Engineering, vol. 95, pp. 349–359. Springer.Google Scholar
Rodríguez, D. & Theofilis, V. 2011 On the birth of stall cells on airfoils. Theor. Comput. Fluid Dyn. 25, 105–117.Google Scholar
Roshko, A.1955 Some measurements of flow in a rectangular cutout. NACA TN 3488.Google Scholar
Rossiter, J. 1964 Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Aero. Res. Counc. R&M 3438.Google Scholar
Rowley, C. W., Colonuis, T. & Basu, A. J. 2002 On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities. J. Fluid Mech. 455, 315–346.Google Scholar
Sarohia, V.1975 Experimental and analytical investigation of oscillations in flows over cavities. PhD thesis, California Institute of Technology.Google Scholar
Sarohia, V. 1977 Experimental investigation of oscillations on flows over shallow cavities. AIAA J. 15, 984–991.Google Scholar
Sun, Y., Nair, A. G., Taira, K., Cattafesta, L. N., Ukeiley, L. S. & Brés, G. A.2014 Numerical simulations of subsonic and transonic open-cavity flows. AIAA Paper 2014-3092.Google Scholar
Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerosp. Sci. 39, 249–315.CrossRefGoogle Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.Google Scholar
Theofilis, V., Hein, S. & Dallmann, U. 2000 On the origins of unsteadiness and three-dimensionality in a laminar separation bubble. Phil. Trans. R. Soc. Lond. A 358, 3229–3246.CrossRefGoogle Scholar
Yamouni, S., Sipp, D. & Jacquin, L. 2013 Interaction between feedback aeroacoustic and acoustic resonance mechanisms in a cavity flow: a global stability analysis. J. Fluid Mech. 717, 134–165.CrossRefGoogle Scholar
Yao, H., Cooper, R. K. & Raghunathan, S. 2004 Numerical simulation of incompressible laminar flow over three dimensional rectangular cavities. Trans. ASME J. Fluids Engng 126, 919–927.Google Scholar
Zhang, K. & Naguib, A. M. 2008 Effect of cavity width on the unsteady pressure in a low-Mach-number cavity. AIAA J. 46, 1878–1880.CrossRefGoogle Scholar
Zhang, K. & Naguib, A. M. 2011 Effect of finite cavity width on flow oscillation in a low-Mach-number cavity. Exp. Fluids 51, 1209–1229.CrossRefGoogle Scholar
Zhang, Y., Sun, Y., Arora, N., Cattafesta, L. N., Taira, K. & Ukeiley, L.2015 Suppression of cavity oscillations via three-dimensonal steady blowing. AIAA Paper 2015-3219.Google Scholar