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Three-dimensional instability in the flow past two side-by-side square cylinders
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10.1063/1.4813628
/content/aip/journal/pof2/25/7/10.1063/1.4813628
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/7/10.1063/1.4813628
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Flow past two square cylinders in a side-by-side arrangement: (a) flow configuration and boundary conditions, and (b) grid system (partially seen near the cylinders at every 4th point for clarity).

Image of FIG. 2.
FIG. 2.

Contours of vorticity components at near-critical conditions. Light and dark colors represent negative and positive values of streamwise vorticity of the Floquet mode, respectively, while solid and dashed lines represent positive and negative values of spanwise vorticity of the base flow, respectively (lines, ω = ±0.1): (a) mode A, Re = 168, = 1.25, and (b) mode B, Re = 202, = 5.6. Reprinted with permission from Choi , Phys. Fluids , 024102 (2012). Copyright 2012, American Institute of Physics.

Image of FIG. 3.
FIG. 3.

Neutral stability curves for flow past a square cylinder. Reprinted with permission from Choi , Phys. Fluids , 024102 (2012). Copyright 2012, American Institute of Physics.

Image of FIG. 4.
FIG. 4.

Patterns of base flow at near-critical conditions for the onset of 3D instability: (a) single object (SO), = 0.2, Re = 59, (b) deflected oscillatory (DO), = 0.6, Re = 68, (c) in-phase (IP), = 1.7, Re = 153, and (d) anti-phase (AP), = 2.5, Re = 158.

Image of FIG. 5.
FIG. 5.

The critical Reynolds number for 3D instability modes plotted against the gap between the two square cylinders. Dashed and chain-dashed lines represent the critical Reynolds numbers of mode A and mode B for flow past a single square cylinder, respectively. The critical Reynolds numbers of SA1 and SA2 have been recalculated based on ′, and plotted with asterisks (*).

Image of FIG. 6.
FIG. 6.

Contours of vorticity components at = 0.2, Re = 59, = 0.65 (mode SA1). Light and dark tones represent negative and positive values of streamwise vorticity of the Floquet mode, respectively, while solid and dashed lines denote positive and negative values of spanwise vorticity of the base flow, respectively: (a) spatial evolution of the Floquet mode (grayscale) superposed on the base flow (lines, ω = ±0.1), and (b) temporal evolution of the Floquet mode at = 4.

Image of FIG. 7.
FIG. 7.

Comparison of time-averaged streamlines: (a) rectangular cylinder with = 2.3 at Re = 50, (b) two square cylinders in the side-by-side arrangement with = 0.3 at Re = 50.

Image of FIG. 8.
FIG. 8.

Contours of vorticity components at = 0.7, Re = 62, = 0.45 (mode SA2). Light and dark tones represent negative and positive values of streamwise vorticity of the Floquet mode, respectively, while solid and dashed lines denote positive and negative values of spanwise vorticity of the base flow, respectively: (a) spatial evolution of the Floquet mode (grayscale) superposed on the base flow (lines, ω = ±0.1, ±0.3), (b) temporal evolution of the Floquet mode at = 8, and (c) temporal evolution of the Floquet mode at = 28.

Image of FIG. 9.
FIG. 9.

Instantaneous streamlines of the base flow at = 0.7, Re = 62 at the same time intervals over one period. The enclosed curve in each figure represents time variation of of the lower cylinder, and the dot indicates the instant at which the corresponding figure is taken: (a) 1/4, (b) 2/4, (c) 3/4, and (d) 4/4.

Image of FIG. 10.
FIG. 10.

Neutral stability curves for the flow past two square cylinders in some selected side-by-side arrangements: = 0.2, mode SA1; 0.6 ≤ ≤ 0.9, mode SA2. The solid line is corresponding to mode A of the single square cylinder case.

Image of FIG. 11.
FIG. 11.

Contours of vorticity components at = 1.7, Re = 153, = 1.45 (mode SA3). Light and dark tones represent negative and positive values of streamwise vorticity of the Floquet mode, respectively, while solid and dashed lines denote positive and negative values of spanwise vorticity of the base flow, respectively: (a) spatial evolution of the Floquet mode (grayscale) superposed on the base flow (lines, ω = ±0.3), (b) temporal evolution of the Floquet mode at = 2, and (c) temporal evolution of the Floquet mode at = 32.

Image of FIG. 12.
FIG. 12.

Contours of vorticity components at = 3.0, Re = 158, = 1.35 (mode SA4). Light and dark tones represent negative and positive values of streamwise vorticity of the Floquet mode, respectively, while solid and dashed lines denote positive and negative values of spanwise vorticity of the base flow, respectively: (a) spatial evolution of the Floquet mode (grayscale) superposed on the base flow (lines, ω = ±0.3), (b) temporal evolution of the Floquet mode at = 2, and (c) temporal evolution of the Floquet mode at = 32.

Image of FIG. 13.
FIG. 13.

Contours of vorticity components at = 2.1, Re = 203, = 5.7 (mode SB4). Light and dark tones represent negative and positive values of streamwise vorticity of the Floquet mode, respectively, while solid and dashed lines denote positive and negative values of spanwise vorticity of the base flow, respectively: (a) spatial evolution of the Floquet mode (grayscale) superposed on the base flow (lines, ω = ±0.1), and (b) temporal evolution of the Floquet mode at = 2.

Image of FIG. 14.
FIG. 14.

Contours of vorticity components at = 1.9, Re = 195, = 5.6 (mode SB3). Light and dark tones represent negative and positive values of streamwise vorticity of the Floquet mode, respectively, while solid and dashed lines denote positive and negative values of spanwise vorticity of the base flow, respectively: (a) spatial evolution of the Floquet mode (grayscale) superposed on the base flow (lines, ω = ±0.1), and (b) temporal evolution of the Floquet mode at = 2.

Image of FIG. 15.
FIG. 15.

The dominant spanwise wavelength at the onset of 3D instability, plotted against the gap between the two cylinders. Dashed and chain-dashed lines represent the critical spanwise wavelengths of mode A and mode B for flow past a single square cylinder, respectively.

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/content/aip/journal/pof2/25/7/10.1063/1.4813628
2013-07-31
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Three-dimensional instability in the flow past two side-by-side square cylinders
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/7/10.1063/1.4813628
10.1063/1.4813628
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