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Research Papers: Flows in Complex Systems

Large Eddy Simulation of Self-Sustained Cavity Oscillation for Subsonic and Supersonic Flows

[+] Author and Article Information
K. M. Nair

Indian Institute of Technology Kanpur,
Kanpur, Uttar Pradesh 208016, India
e-mail: muralird@iitk.ac.in

S. Sarkar

Professor
Mem. ASME
Indian Institute of Technology Kanpur,
Kanpur, Uttar Pradesh 208016, India
e-mail: subra@iitk.ac.in

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 17, 2015; final manuscript received July 26, 2016; published online October 18, 2016. Assoc. Editor: Elias Balaras.

J. Fluids Eng 139(1), 011102 (Oct 18, 2016) (13 pages) Paper No: FE-15-1493; doi: 10.1115/1.4034371 History: Received July 17, 2015; Revised July 26, 2016

The primary objective is to perform a large eddy simulation (LES) using shear improved Smagorinsky model (SISM) to resolve the large-scale structures, which are primarily responsible for shear layer oscillations and acoustic loads in a cavity. The unsteady, three-dimensional (3D), compressible Navier–Stokes (N–S) equations have been solved following AUSM+-up algorithm in the finite-volume formulation for subsonic and supersonic flows, where the cavity length-to-depth ratio was 3.5 and the Reynolds number based on cavity depth was 42,000. The present LES resolves the formation of shear layer, its rollup resulting in large-scale structures apart from shock–shear layer interactions, and evolution of acoustic waves. It further indicates that hydrodynamic instability, rather than the acoustic waves, is the cause of self-sustained oscillation for subsonic flow, whereas the compressive and acoustic waves dictate the cavity oscillation, and thus the sound pressure level for supersonic flow. The present LES agrees well with the experimental data and is found to be accurate enough in resolving the shear layer growth, compressive wave structures, and radiated acoustic field.

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Figures

Grahic Jump Location
Fig. 1

(a) Details of computational domain and (b) imposed boundary conditions

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Fig. 2

Profiles of streamwise (a) time-averaged velocity (u¯) and (b) TKE at different locations (x/d = 6.4, 7.2, and 8.4) for different levels of grids such as grid 1 (360 × 220 × 64), grid 2 (400 × 300 × 64), and grid 3 (460 × 300 × 64), respectively

Grahic Jump Location
Fig. 3

Comparison of profiles of (a) time-averaged streamwise (u¯), (b) normal velocities (v¯), (c) streamwise (vrms), and (d) normal velocity (vrms) fluctuations with data of Forestier et al. [7] for eight streamwise locations at 8%, 20%, 32%, 44%, 56%, 68%, 80%, and 92% of cavity length. Circle represents the experiment and the line denotes the LES.

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Fig. 4

Contours of vorticity magnitude superimposed with pressure (values are limited to 1.0–2.0 in steps of 21) for four instances illustrating aerodynamic instability and shear layer dynamics for M = 0.6

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Fig. 5

Contours of instantaneous pressure illustrating development of pressure perturbations near aft wall due to vortex–edge interaction for M = 0.6

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Fig. 6

The contours of density gradient magnitude during a vortex-shedding cycle illustrating self-sustained oscillation in a cavity for M = 0.6

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Fig. 7

Contours of vorticity magnitude superimposed with pressure lines (values are limited to 0.7–2.0 in steps of 11) for M = 1.7 depicting acoustic feedback mechanism and shock–shear layer interaction

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Fig. 8

Contours of divergence of velocity (Div u) superimposed with vorticity illustrating the role of shock–shear layer interaction and acoustic feedback waves in sustaining oscillation for M = 1.7. Arrow shows the direction of propagation.

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Fig. 9

Instantaneous contours of |∇ρ| demonstrating the excitation of shear layer by reflected feedback waves developing large-scale coherent eddies and the features of supersonic flow. Arrow shows the direction of propagation.

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Fig. 10

Mach contours (values are limited to 1.0–2.0 in steps of 21) superimposed with vorticity for four instances during a vortex-shedding cycle demonstrating shock–shear layer interaction for M = 1.7

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Fig. 11

Trajectory of large-scale eddies within the cavity superimposed with the pressure traces from a point P (8.5d, −0.1d) on the aft wall for two time periods: (a) M = 0.6 and (b)M = 1.7. (Δt indicates time lag between impingement and maximum pressure generation.)

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Fig. 12

The power spectra of vertical velocity along the shear layer for five streamwise locations at x/d = 5.7, 6.4, 7.2, 7.8, and 8.4 (20%, 40%, 60%, 80%, and 96% of cavity length): (a) M = 0.6 and (b) M = 1.7. Strouhal number and amplitude of dominant modes are given inside the bracket.

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Fig. 13

Isosurface of instantaneous Q-criterion corresponding to the value of 5.0 for two instants during a vortex-shedding cycle for M = 0.6: (a) t/T = 0.50 and (b) t/T = 0.75

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Fig. 14

Isosurface of instantaneous Q-criterion corresponding to the value of 2.0 for two instants during a vortex-shedding cycle for M = 1.7: (a) t/T = 0.50 and (b) t/T = 1.0

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Fig. 15

The evolutions of TKE (shown in flood) superimposed with its production (indicated by lines) for (a) M = 0.6 and (b) M = 1.7

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Fig. 16

Velocity profiles extracted from the simulations at three streamwise locations (corresponding to 20%, 40%, and 60% of cavity length), superimposed with their respective analytic profiles: (a) x/d = 5.7 (A = 0.647 and B = 0.862), (b) x/d = 6.4 (A = 0.763 and B = 0.683), and (c) x/d = 7.2 (A = 0.868 and B = 0.603) for M = 0.6

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