Skip to main content
×
Home
    • Aa
    • Aa

Three-dimensional instabilities in compressible flow over open cavities

  • GUILLAUME A. BRÈS (a1) and TIM COLONIUS (a1)
Abstract

Direct numerical simulations are performed to investigate the three-dimensional stability of compressible flow over open cavities. A linear stability analysis is conducted to search for three-dimensional global instabilities of the two-dimensional mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of flow conditions and cavity aspect ratios. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately one cavity depth and oscillates with a frequency about one order of magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities previously reported in flows over backward-facing steps, lid-driven cavity flows and Couette flows. Results from three-dimensional simulations of the nonlinear compressible Navier–Stokes equations are also reported. The formation of oscillating (and, in some cases, steady) spanwise structures is observed inside the cavity. The spanwise wavelength and oscillation frequency of these structures agree with the linear analysis predictions. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. The results are consistent with observations of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows.

Copyright
References
Hide All
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. Tech. Rep. CR-4653. NASA.
Aidun C. K., Triantafillopoulos N. G. & Benson J. D. 1991 Global stability of a lid-driven cavity with throughflow: Flow visualization studies. Phys. Fluids A 3, 20812091.
Albensoeder S. & Kuhlmann H. C. 2006 Nonlinear three-dimensional flow in the lid-driven square cavity. J. Fluid Mech. 569, 465480.
Albensoeder S., Kuhlmann H. C. & Rath H. J. 2001 Three-dimensional centrifugal-flow instabilities in the lid-driven-cavity problem. Phys. Fluids 13, 121135.
Alvarez J., Kerschen E. & Tumin A. 2004 A theoretical model for cavity acoustic resonances in subsonic flow. AIAA Paper 2004-2845.
Armaly B. F, Durst F., Pereira J. C. F. & Schönung B. 1983 Experimental and theoritical investigation of backward-facing step flow. J. Fluid Mech. 127, 473496.
Barkley D., Gomes G. M & Henderson R. D. 2002 Three-dimensional instability in flow over a backward-facing step. J. Fluid Mech. 473, 167190.
Bayly B. J. 1988 Three-dimensional centrifugal-type instabilities in inviscid two-dimensional flows. Phys. Fluids 31, 5664.
Benson J. D. & Aidun C. K. 1992 Transition to unsteady nonperiodic state in a through-flow lid-driven cavity. Phys. Fluids A 4, 2316–2319.
Brès G. A. 2007 Numerical simulations of three-dimensional instabilities in cavity flows. PhD thesis, California Institute of Technology.
Brès G. A. & Colonius T. 2007 Three-dimensional linear stability analysis of cavity flows. AIAA Paper 2007-1126.
Cattafesta L. N. III, Garg S., Kegerise M. S. & Jones G. S. 1998 Experiments on compressible flow-induced cavity oscillations. AIAA Paper 98-2912.
Cattafesta L. N. III, Shukla D., Garg S. & Ross J. A. 1999 Development of an adaptive weapons-bay suppression system. AIAA Paper 99–1901.
Chang K., Constantinescu G. & Park S. 2006 Analysis of the flow and mass transfer processes for the incompressible flow past an open cavity with a laminar and a fully turbulent incoming boundary layer. J. Fluid Mech. 561, 113145.
Chatellier L., Laumonier J. & Gervais Y. 2006 Theoretical and experimental investigation of low Mach number turbulent cavity flows. Exps. Fluids 36, 728740.
Colonius T. 2001 An overview of simulation, modeling, and active control of flow/acoustic resonance in open cavities. AIAA Paper 2001–0076.
Colonius T., Lele S. K. & Moin P. 1993 Boundary conditions for direct computation of aerodynamic sound. AIAA J. 31, 15471582.
Ding Y. & Kawahara M. 1999 Three-dimensional linear stability of incompressible viscous flow using the finite element method. Intl J. Numer. Meth. Fluids 31, 451479.
DiPrima R. C., Eagles P. M. & Ng B. S. 1984 The effect of radius ratio on the stability of Couette flow and Taylor vortex flow. Phys. Fluids 27, 24032411.
Drazin P. G. & Reid W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Faure T. M., Adrianos P., Lusseyran F. & Pastur L. 2007 Visualizations of the flow inside an open cavity at medium range Reynolds numbers. Exps. Fluids 42, 169184.
Forestier N., Jacquin L. & Geffroy P. 2003 The mixing layer over a deep cavity at high-subsonic speed. J. Fluid Mech. 475, 101145.
Freund J. B. 1997 Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound. AIAA J. 35, 740742.
Frigo M. & Johnson S. G. 2007 FFTW library. Website: http://www.fftw.org.
Gharib M. & Roshko A. 1987 The effect of flow oscillations on cavity drag. J. Fluid Mech. 177, 501530.
Kegerise M. A., Spina E. F., Garg S. & Cattafesta L. N. III 2004 Mode-switching and nonlinear effects in compressible flow over a cavity. Phys. Fluids 16, 678687.
Larchevêque L., Sagaut P. & Labbé O. 2007 Large-eddy simulation of a subsonic cavity flow including asymmetric three-dimensional effects. J. Fluid Mech. 577, 105126.
Larchevêque L., Sagaut P., Lê T. & Comte P. 2004 Large-eddy simulation of a compressible flow in a three-dimensional open cavity at high Reynolds number. J. Fluid Mech. 516, 265301.
Larchevêque L., Sagaut P., Mary I., Labbé O. & Comte P. 2003 Large-eddy simulation of a compressible flow past a deep cavity. Phys. Fluids 15, 193210.
Lehoucq R., Maschhoff K., Sorensen D. & Yang C. 2007 ARPACK software. Website: http://www.caam.rice.edu/software/ARPACK/.
Lele S. K. 1992 Compact finite difference scheme with spectral-like resolution. J. Comput. Phys. 103, 1642.
Maull D. J. & East L. F. 1963 Three-dimensional flow in cavities. J. Fluid Mech. 16, 620632.
Neary M. D. & Stephanoff M. D. 1987 Shear-layer-driven transition in a rectangular cavity. Phys. Fluids 30, 29362946.
Podvin B., Fraigneau Y., Lusseyran F. & Gougat P. 2006 A reconstruction method for the flow past an open cavity. Trans. ASME: J. Fluids Engng 128, 531540.
Poinsot T. J. & Lele S. K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101, 104129.
Ramanan N. & Homsy G. M. 1994 Linear stability of lid-driven cavity flow. Phys. Fluids 6, 26902701.
Rizzetta D. P. & Visbal M. R. 2003 Large-eddy simulation od supersonic cavity flowfields including flow control. AIAA J. 41, 14521462.
Rockwell D. & Knisely C. 1980 Observations of the three-dimensional nature of unstable flow past a cavity. Phys. Fluids 23, 425431.
Rockwell D. & Naudascher E. 1978 Review — self-sustaining oscillations of flow past cavities. Trans. ASME: J. Fluids Engng 100.
Rossiter J. E. 1964 Wind–tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Tech. Rep. 3438. ARC.
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, 315346.
Rowley C. W. & Williams D. R. 2006 Dynamics and control of high-Reynolds-number flow over open cavities. Annu. Rev. Fluid Mech. 38, 251276.
Rowley C. W., Williams D. R., Colonius T., Murray R. M. & MacMynowski D. G. 2006 Linear models for control of cavity flow oscillations. J. Fluid Mech. 547, 317330.
Sarohia V. 1975 Experimental and analytical investigation of oscillations in flows over cavities. PhD thesis, California Institute of Technology.
Theofilis V. & Colonius T. 2003 An algorithm for the recovery of 2- and 3-D biglobal instabilities of compressible flow over 2-D open cavities. AIAA Paper 2003-4143.
Theofilis V., Duck P. W. & Owen J. 2004 Viscous linear stability analysis of rectangular duct and cavity flows. J. Fluid Mech. 505, 249286.
Thompson K. W. 1990 Time-dependent boundary conditions for hyperbolic systems, II. J. Comput. Phys. 89, 439461.
Williams P. T. & Baker A. J. 1997 Numerical simulations of laminar flow over a 3D backward-facing step. Intl J. Numer. Meth. Fluids 24, 11591183.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 1
Total number of PDF views: 144 *
Loading metrics...

Abstract views

Total abstract views: 281 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st October 2017. This data will be updated every 24 hours.