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Interaction between feedback aeroacoustic and acoustic resonance mechanisms in a cavity flow: a global stability analysis

Published online by Cambridge University Press:  01 February 2013

Sami Yamouni ,
Denis Sipp  and
Laurent Jacquin
Sami Yamouni*
Affiliation:
ONERA DAFE, 8 rue des Vertugadins, 92190 Meudon, France
Denis Sipp
Affiliation:
ONERA DAFE, 8 rue des Vertugadins, 92190 Meudon, France
Laurent Jacquin
Affiliation:
ONERA DAFE, 8 rue des Vertugadins, 92190 Meudon, France
*
†Email address for correspondence: [email protected]
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Abstract

We perform a global stability analysis of a flow over an open cavity, characterized by a Reynolds number, based on the upstream velocity and the cavity length, of $7500$. We compute base flows and unstable global modes of the flow for different Mach numbers ranging from $0$ to $0. 9$. In the incompressible regime ($M= 0$), we show that the flow is subject to global instabilities due to Kelvin–Helmholtz instabilities in the shear layer, which become strengthened by a hydrodynamic pressure feedback. The influence of the boundary-layer thickness and of the length-to-depth ratio of the cavity on these shear-layer modes has been investigated. In the compressible regime ($M\gt 0$), we have shown that all unstable global modes are continuously connected to the incompressible shear-layer modes as $M\rightarrow 0$. These shear-layer modes correspond to the beginning of branches of global modes, whose frequencies evolve (as a function of the Mach number), in accordance with the feedback aeroacoustic mechanism (Rossiter, Tech. Rep. Aero. Res. Counc. R. & M., 1964). We have also identified branches of global modes behaving in agreement with acoustic resonance mechanisms (East, J. Sound Vib., vol. 3, 1966, pp. 277–287; Tam, J. Sound Vib., vol. 49, 1976, pp. 353–364; Koch, AIAA J., vol. 43, 2005, pp. 2342–2349). At the intersections between both types of branches, the growth rate of the global modes is seen to display a local maximum. Along the aeroacoustic feedback branches, the number of vortical structures in the shear layer is kept constant, while the pressure pattern inside the cavity is conserved along the acoustic resonance branches. We show that both the feedback aeroacoustic and acoustic resonance mechanisms are at play over the entire subsonic regime, from $M= 0$ to $M= 0. 9$. At low Mach numbers, we suggest that it is still the feedback aeroacoustic mechanism that selects the frequency, even though the fundamental acoustic resonance mode is also important due to enhancing the response. At higher Mach numbers, we observe that the pressure pattern of the acoustic resonance modes (fundamental acoustic modes, first longitudinal acoustic modes, first longitudinal-depth acoustic modes) inside the cavity determines the directivity of the radiated noise. Links with experimental results are finally discussed.

JFM classification

Compressible Flows: Compressible Flows Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 717 , 25 February 2013 , pp. 134 - 165
Copyright
©2013 Cambridge University Press

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References

Ahuja, K. K. & Mendoza, J. 1995 Effects of cavity dimensions, boundary layer, and temperature on cavity noise with emphasis on benchmark data to validate computational aeroacoustic codes. NASA Contractor Report 4653.Google Scholar
Alvarez, J. O., Kerschen, E. J. & Tumin, A. 2004 A theoretical model for cavity acoustic resonances in subsonic flow. AIAA Paper 2845.Google Scholar
Amestoy, P. R., Duff, I. S., Koster, J. & L’Excellent, J.-Y 2001 A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Applics 23 (1), 15–41.CrossRefGoogle Scholar
Barbagallo, A., Sipp, D. & Schmid, P. 2009 Closed-loop control of an open cavity flow using reduced order models. J. Fluid Mech. 641, 1–50.Google Scholar
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75 (5), 750.CrossRefGoogle 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.CrossRefGoogle Scholar
Bilanin, A. J. & Covert, E. E. 1973 Estimation of possible excitation frequencies for shallow rectangular cavities. AIAA J. 11 (3), 347–351.CrossRefGoogle Scholar
Blake, W. K. 1986 Mechanics of Flow-induced Sound and Vibration. Academic.Google Scholar
Block, P. J. W. 1976 Noise response of cavities of varying dimensions at subsonic speeds. Tech. Rep. D-8351. NASA Tech. Note.Google Scholar
Brès, G. A. & Colonius, T. 2008 Three-dimensional instabilities in compressible flow over open cavities. J. Fluid Mech. 599, 309–339.CrossRefGoogle Scholar
Candel, S. M. 1992 Combustion instabilities coupled by pressure waves and their active control. In Symposium (International) on Combustion, vol. 24. pp. 1277–1296. Elsevier.Google Scholar
Chedevergne, F., Casalis, G. & Féraille, T. 2006 Biglobal linear stability analysis of the flow induced by wall injection. Phys. Fluids 18, 014103.Google Scholar
Colonius, T. 2004 Modelling artificial boundary conditions for compressible flow. Annu. Rev. Fluid Mech. 36, 315–345.CrossRefGoogle Scholar
Craik, A. D. D. 1988 Wave Interactions and Fluid Flows. Cambridge University Press.Google Scholar
Crouch, J. D., Garbaruk, A. & Magidov, D. 2007 Predicting the onset of flow unsteadiness based on global instability. J. Comput. Phys. 224 (2), 924–940.Google Scholar
Crouch, J. D., Garbaruk, A., Magidov, D. & Travin, A. 2009 Origin of transonic buffet on aerofoils. J. Fluid Mech. 628, 357.Google Scholar
Curle, N. 1955 The influence of solid boundaries upon aerodynamic sound. Proc. R. Soc. Lond. Ser. A. Mathematical and Physical Sciences 231 (1187), 505–514.Google Scholar
East, L. F. 1966 Aerodynamically induced resonance in rectangular cavities. J. Sound Vib. 3, 277–287.CrossRefGoogle 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.CrossRefGoogle Scholar
Gharib, M. & Roshko, A. 1987 The effect of flow oscillations on cavity drag. J. Fluid Mech. 177, 501–530.Google Scholar
Howe, M. S. 2004 Mechanism of sound generation by low Mach number flow over a wall cavity. J. Sound Vib. 273 (1–2), 103–123.Google Scholar
Jackson, C. P. 1987 A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech. 182 (1), 23–45.Google Scholar
Koch, W. 2005 Acoustic resonances in rectangular open cavities. AIAA J. 43 (11), 2342–2349.Google Scholar
Krishnamurty, K. 1956 Sound radiation from surface cutouts in high speed flow. PhD thesis, California Institute of Technology.Google Scholar
Larcheveque, L., Sagaut, P., Mary, I., Labbé, O. & Comte, P. 2003 Large-eddy simulation of a compressible flow past a deep cavity. Phys. Fluids 15, 193.Google Scholar
Lehoucq, R. B. 1995 Deflation techniques for an implicitly re-started arnoldi iteration. Tech. Rep. DTIC document.Google Scholar
Mack, C. J., Schmid, P. J. & Sesterhenn, J. L. 2008 Global stability of swept flow around a parabolic body: connecting attachment-line and crossflow modes. J. Fluid Mech. 611 (1), 205–214.Google Scholar
Meliga, P. 2008 A theoretical approach for the onset and control of unsteadiness in compressible afterbody flows. PhD thesis, Ecole Polytechnique.Google Scholar
Meliga, P., Sipp, D. & Chomaz, J. M. 2010 Effect of compressibility on the global stability of axisymmetric wake flows. J. Fluid Mech. 660, 499–526.Google Scholar
Mery, F. & Casalis, G. 2011 Innovative tool for realistic cavity flow analysis: global stability. In Proceedings of the Sixth International Conference on Computational Fluid Dynamics, ICCFD6, St Petersburg, Russia, on July 12–16 2010, p. 449 Springer.Google Scholar
Miles, J. W. 1958 On the disturbed motion of a plane vortex sheet. J. Fluid Mech. 4 (Pt 5), 538–552.CrossRefGoogle Scholar
Monkewitz, P. A., Huerre, P. & Chomaz, J. M. 1993 Global linear stability analysis of weakly non-parallel shear flows. J. Fluid Mech. 251, 1–20.CrossRefGoogle Scholar
Pavithran, S. & Redekopp, L. G. 1989 The absolute-convective transition in subsonic mixing layers. Phys. Fluids A: Fluid Dynamics 1, 1736.Google Scholar
Plumblee, H. E., Gibson, J. S. & Lassiter, L. W. 1962 A theoretical and experimental investigation of the acoustic response of cavities in aerodynamic flow. Tech. Rep. WADD-TR-62-75. U.S. Air Force Rep.Google Scholar
Robinet, J. C. 2007 Bifurcations in shock-wave/laminar-boundary-layer interaction: global instability approach. J. Fluid Mech. 579 (1), 85–112.Google Scholar
Rockwell, D. & Knisely, C. 1979 The organized nature of flow impingement upon a corner. J. Fluid Mech. 93 (03), 413–432.Google Scholar
Rockwell, D. & Naudascher, E. 1978 Review self-sustaining oscillations of flow past cavities. J. Fluids Engng 100, 152.Google Scholar
Rockwell, D. & Schachenmann, A. 1982 Self-generation of organized waves in an impinging turbulent jet at low Mach number. J. Fluid Mech. 117 (1), 425–441.CrossRefGoogle Scholar
Rossiter, J. E. 1964 Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Tech. Rep. Aero. Res. Counc. R. & M.Google Scholar
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.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 in flows over shallow cavities. AIAA J. 15 (7), 984–991.Google Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Applied Mathematical Sciences, vol. 142 , Springer.Google Scholar
Sipp, D. & Lebedev, A. 2007 Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333–358.Google Scholar
Sipp, D., Marquet, O., Meliga, P. & Barbagallo, A. 2010 Dynamics and control of global instabilities in open-flows: a linearized approach. Appl. Mech. Rev. 63, 030801.Google Scholar
Tam, C. K. W. 1976 The acoustic modes of a two-dimensional rectangular cavity. J. Sound Vib. 49, 353–364.Google Scholar
Tam, C. K. W. & Block, P. J. W. 1978 Tones induced by flow over cavities. J. Fluid Mech. 89, 373–399.Google Scholar
Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerosp. Sci. 39 (4), 249–316.Google Scholar
Yang, Y., Rockwell, D., Lai-Fook Cody, K. & Pollack, M. 2009 Generation of tones due to flow past a deep cavity: effect of streamwise length. J. Fluids Struct. 25 (2), 364–388.Google Scholar

Yamouni et al. supplementary movie

Movie of iso-contours of pressure evolving in time over 3 time-periods for the mode 4a (σ=1.46, St=2.07)

Download Yamouni et al. supplementary movie(Video)
Video 2.7 MB

Yamouni et al. supplementary movie

Movie of iso-contours of pressure evolving in time over 3 time-periods for the mode 4b (σ=1.2, St=1.96)

Download Yamouni et al. supplementary movie(Video)
Video 2.6 MB

Yamouni et al. supplementary movie

Movie of iso-contours of pressure evolving in time over 3 time-periods for the mode 5c (σ=1.47, St=1.86)

Download Yamouni et al. supplementary movie(Video)
Video 2.6 MB