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Three-dimensional instabilities in compressible flow over open cavities


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.

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C. K. Aidun , N. G. Triantafillopoulos & J. D. Benson 1991 Global stability of a lid-driven cavity with throughflow: Flow visualization studies. Phys. Fluids A 3, 20812091.

S. Albensoeder , H. C. Kuhlmann & H. J. Rath 2001 Three-dimensional centrifugal-flow instabilities in the lid-driven-cavity problem. Phys. Fluids 13, 121135.

B. J. Bayly 1988 Three-dimensional centrifugal-type instabilities in inviscid two-dimensional flows. Phys. Fluids 31, 5664.

J. D. Benson & C. K. Aidun 1992 Transition to unsteady nonperiodic state in a through-flow lid-driven cavity. Phys. Fluids A 4, 2316–2319.

L. Chatellier , J. Laumonier & Y. Gervais 2006 Theoretical and experimental investigation of low Mach number turbulent cavity flows. Exps. Fluids 36, 728740.

T. Colonius , S. K. Lele & P. Moin 1993 Boundary conditions for direct computation of aerodynamic sound. AIAA J. 31, 15471582.

Y. Ding & M. Kawahara 1999 Three-dimensional linear stability of incompressible viscous flow using the finite element method. Intl J. Numer. Meth. Fluids 31, 451479.

R. C. DiPrima , P. M. Eagles & B. S. Ng 1984 The effect of radius ratio on the stability of Couette flow and Taylor vortex flow. Phys. Fluids 27, 24032411.

T. M. Faure , P. Adrianos , F. Lusseyran & L. Pastur 2007 Visualizations of the flow inside an open cavity at medium range Reynolds numbers. Exps. Fluids 42, 169184.

J. B. Freund 1997 Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound. AIAA J. 35, 740742.

M. A. Kegerise , E. F. Spina , S. Garg & L. N. Cattafesta III 2004 Mode-switching and nonlinear effects in compressible flow over a cavity. Phys. Fluids 16, 678687.

L. Larchevêque , P. Sagaut , I. Mary , O. Labbé & P. Comte 2003 Large-eddy simulation of a compressible flow past a deep cavity. Phys. Fluids 15, 193210.

S. K. Lele 1992 Compact finite difference scheme with spectral-like resolution. J. Comput. Phys. 103, 1642.

M. D. Neary & M. D. Stephanoff 1987 Shear-layer-driven transition in a rectangular cavity. Phys. Fluids 30, 29362946.

T. J. Poinsot & S. K. Lele 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101, 104129.

N. Ramanan & G. M. Homsy 1994 Linear stability of lid-driven cavity flow. Phys. Fluids 6, 26902701.

D. P. Rizzetta & M. R. Visbal 2003 Large-eddy simulation od supersonic cavity flowfields including flow control. AIAA J. 41, 14521462.

D. Rockwell & C. Knisely 1980 Observations of the three-dimensional nature of unstable flow past a cavity. Phys. Fluids 23, 425431.

C. W. Rowley & D. R. Williams 2006 Dynamics and control of high-Reynolds-number flow over open cavities. Annu. Rev. Fluid Mech. 38, 251276.

K. W. Thompson 1990 Time-dependent boundary conditions for hyperbolic systems, II. J. Comput. Phys. 89, 439461.

P. T. Williams & A. J. Baker 1997 Numerical simulations of laminar flow over a 3D backward-facing step. Intl J. Numer. Meth. Fluids 24, 11591183.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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