Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-17T11:25:06.070Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical investigation of the saturation process in an incompressible cavity flow

Published online by Cambridge University Press:  20 December 2017

N. Vinha Open the ORCID record for N. Vinha [Opens in a new window] ,
F. Meseguer-Garrido ,
J. de Vicente  and
E. Valero
N. Vinha*
Affiliation:
School of Aerospace Engineering, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
F. Meseguer-Garrido
Affiliation:
School of Aerospace Engineering, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
J. de Vicente
Affiliation:
School of Aerospace Engineering, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
E. Valero
Affiliation:
School of Aerospace Engineering, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A numerical study of the saturation process inside a rectangular open cavity is presented. Previous experiments and linear stability analysis of the problem completely described the flow in its onset, as well as in a saturated regime, characterized by three-dimensional centrifugal modes. The morphology of the modes found in the experiments matched the ones predicted by linear analysis, but with a shift in frequencies for the oscillating modes. A three-dimensional incompressible direct numerical simulation (DNS) is employed for a detailed investigation of the saturation process inside a cavity with dimensions similar to the one used in the experiments, to further explain the behaviour of these modes. In this work, periodic boundary conditions are first imposed to better understand the effect of the saturation process far from the walls. Then, the effects of spanwise solid wall boundary conditions are investigated with a DNS reproducing the full dynamics of the experiments. The main flow structures are identified using the dynamic mode decomposition technique and compared with previous experimental and linear stability analysis results. The main reason for the aforementioned shift in frequency is explained in this paper, as it is a function of the velocity of the main recirculating vortex.

JFM classification

Mathematical Foundations: Computational methods Instability: Instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , pp. 182 - 209
Copyright
© 2017 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.)

References

Albensoeder, S. & Kuhlmann, H. C. 2006 Nonlinear three-dimensional flow in the lid-driven square cavity. J. Fluid Mech. 569, 465–480.Google Scholar
Albensoeder, S., Kuhlmann, H. C. & Rath, H. J. 2001 Three-dimensional centrifugal-flow instabilities in the lid-driven-cavity problem. Phys. Fluids 13 (1), 121–135.Google Scholar
Bagheri, S. 2013 Koopman-mode decomposition of the cylinder wake. J. Fluid Mech. 726, 596–623.Google Scholar
Barkley, D., Gomes, G. M. & Henderson, R. D. 2002 Three-dimensional instability in flow over a backward-facing step. J. Fluid Mech. 473, 167–190.Google Scholar
Basley, J.2012 An experimental investigation on waves and coherent structures in a three-dimensional open cavity flow. PhD thesis, Université Paris Sud & Monash University.Google Scholar
Basley, J., Pastur, L. R., Lusseyran, F., Faure, T. M. & Delprat, N. 2011 Experimental investigation of global structures in an incompressible cavity flow using time-resolved PIV. Exp. Fluids 50 (4), 905–918.Google Scholar
Basley, J., Pastur, L. R., Lusseyran, F., Soria, J. & Delprat, N. 2014 On the modulating effect of three-dimensional instabilities in open cavity flows. J. Fluid Mech. 759, 546–578.Google Scholar
Brès, G. A. & Colonius, T. 2008 Three-dimensional instabilities in compressible flow over open cavities. J. Fluid Mech. 599, 309–339.Google Scholar
le Clainche, S. & Vega, J. M. 2017 Higher order dynamic mode decomposition to identify and extrapolate flow patterns. Phys. Fluids 29 (8), 084102.Google Scholar
Dawson, S. T. M., Hemati, M. S., Williams, M. O. & Rowley, C. W. 2016 Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition. Exp. Fluids 57 (3), 42.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.Google Scholar
Duke, D., Soria, J. & Honnery, D. 2012 An error analysis of the dynamic mode decomposition. Exp. Fluids 52 (2), 529–542.Google 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 (2), 169–184.Google Scholar
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 (3), 395–410.Google Scholar
Ferrer, E., de Vicente, J. & Valero, E. 2014 Low cost 3d global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools. Intl J. Numer. Meth. Fluids 76 (3), 169–184.Google Scholar
Floryan, J. M. 1991 On the Görtler instability of boundary layers. Prog. Aerosp. Sci. 28 (3), 235–271.Google Scholar
Gómez, F., Le Clainche, S., Paredes, P., Hermanns, M. & Theofilis, V. 2012 Four decades of studying global linear instability: progress and challenges. AIAA J. 50 (12), 2731–2743.Google Scholar
González, L. M., Ahmed, M., Kühnen, J., Kuhlmann, H. C. & Theofilis, V. 2011 Three-dimensional flow instability in a lid-driven isosceles triangular cavity. J. Fluid Mech. 675, 369–396.Google Scholar
Guermond, J.-L., Migeon, C., Pineau, G. & Quartapelle, L. 2002 Start-up flows in a three-dimensional rectangular driven cavity of aspect ratio 1:1:2 at Re = 1000. J. Fluid Mech. 450, 169–199.Google Scholar
Jacobs, G., Kopriva, D. & Mashayek, F. 2005 Validation study of a multidomain spectral code for simulation of turbulent flows. AIAA J. 43 (6), 1256–1264.Google Scholar
Knisely, C. & Rockwell, D. 1982 Self-sustained low-frequency components in an impinging shear layer. J. Fluid Mech. 116, 157–186.Google Scholar
Kopriva, D. 1998 A staggered-grid multidomain spectral method for the compressible Navier–Stokes equations. J. Comput. Phys. 143 (1), 125–158.Google Scholar
Kopriva, D. 2009 Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers. Springer.Google Scholar
Koseff, J. R. & Street, R. L. 1984 On end wall effects in a lid-driven cavity flow. Trans. ASME J. Fluids Engng 106 (4), 385–389.Google Scholar
Kuhlmann, H. C., Wanschura, M. & Rath, H. J. 1997 Flow in two-sided lid-driven cavities: non-uniqueness, instabilities, and cellular structures. J. Fluid Mech. 336, 267–299.Google Scholar
Meseguer-Garrido, F., de Vicente, J., Valero, E. & Theofilis, V. 2014 On linear instability mechanisms in incompressible open cavity flow. J. Fluid Mech. 752, 219–236.Google Scholar
Mezic, I. 2013 Analysis of fluid flows via spectral properties of the Koopman operator. Annu. Rev. Fluid Mech. 45, 357–378.Google Scholar
Migeon, C. 2002 Details on the start-up development of the Taylor–Gortler-like vortices inside a square-section lid-driven cavity for 1000⩽Re⩽3200. Exp. Fluids 33 (4), 594–602.Google Scholar
Migeon, C., Pineau, G. & Texier, A. 2003 Three-dimensionality development inside standard parallelepipedic lid-driven cavities at Re = 1000. J. Fluids Struct. 17 (5), 717–738.Google Scholar
Neary, M. D. & Stephanoff, K. D. 1987 Shear-layer-driven transition in a rectangular cavity. Phys. Fluids 30 (10), 2936–2946.Google Scholar
Powell, A. 1953 On edge tones and associated phenomena. Acustica 3, 233–243.Google Scholar
Powell, A. 1961 On the edgetone. J. Acoust. Soc. Am. 33 (4), 395–409.Google Scholar
Ramanan, N. & Homsy, G. M. 1994 Linear stability of lid-driven cavity flow. Phys. Fluids 6 (8), 2690–2701.Google Scholar
Richecoeur, F., Hakim, L., Renaud, A. & Zimmer, L. 2012 DMD algorithms for experimental data processing in combustion. In Proceedings of the Summer Program 2012, pp. 459–468. Center for Turbulence Research, Stanford University.Google Scholar
Rockwell, D. 1977 Prediction of oscillation frequencies for unstable flow past cavities. Trans. ASME J. Fluids Engng 99 (2), 294–299.Google Scholar
Rockwell, D. & Knisely, C. 1980 Observations of the three-dimensional nature of unstable flow past a cavity. Phys. Fluids 23 (3), 425–431.Google Scholar
Rockwell, D. & Naudascher, E. 1979 Self-sustained oscillations of impinging free shear layers. Annu. Rev. Fluid Mech. 11, 67–94.Google Scholar
Rossiter, J. E. 1964 Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Aeronautical Research Council Reports and Memoranda 3438, 1–32.Google Scholar
Rowley, C., Mezic, I., Bagheri, S., Schlatter, P. & Henningson, D. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115–127.Google Scholar
Sarohia, V. 1977 Experimental investigation of oscillations in flows over shallow cavities. AIAA J. 15 (7), 984–991.Google Scholar
Schmid, P. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.Google Scholar
Schmid, P. 2013 Dynamic Mode Decomposition, von Karman Institute Lecture Series on Advanced Post-Processing of Experimental and Numerical Data. von Karman Institute for Fluid Dynamics.Google Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.Google Scholar
Seena, A. & Sung, H. J. 2011 Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations. Intl J. Heat Fluid Flow 32, 1098–1110.Google Scholar
Shankar, P. N. & Deshpande, M. D. 2000 Fluid mechanics in the driven cavity. Annu. Rev. Fluid Mech. 32, 93–136.Google Scholar
Sipp, D. & Jacquin, L. 2000 Three-dimensional centrifugal-type instabilities of two-dimensional flows in rotating systems. Phys. Fluids 12 (7), 1740–1748.Google Scholar
Theofilis, V. & Colonius, T.2004 Three-dimensional instablities of compressible flow over open cavities: direct solution of the biglobal eigenvalue problem. Proceedings of the 34th AIAA Fluid Dynamics Conference and Exhibit, Portland, OR, AIAA Paper 2004–2544.Google Scholar
Theofilis, V., Duck, P. W. & Owen, J. 2004 Viscous linear stability analysis of rectangular duct and cavity flows. J. Fluid Mech. 505, 249–286.Google Scholar
de Vicente, J., Basley, J., Meseguer-Garrido, 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
de Vicente, J., Rodríguez, D., Theofilis, V. & Valero, E. 2011 Stability analysis in spanwise-periodic double-sided lid-driven cavity flows with complex cross-sectional profiles. Comput. Fluids 43 (1), 143–153.Google Scholar
Vinha, N., Meseguer-Garrido, F., de Vicente, J. & Valero, E. 2016 A dynamic mode decomposition of the saturation process in the open cavity flow. Aerosp. Sci. Technol. 52, 198–206.Google 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.Google Scholar
Ziada, S. & Rockwell, D. 1982 Oscillations of an unstable mixing layer impinging upon an edge. J. Fluid Mech. 124, 307–334.Google Scholar