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Research Papers: Fluid-Structure Interaction

# A Parametric Study of the Resonance Mechanism of Two Tandem Cylinders in Cross-Flow

[+] Author and Article Information
A. Mohany2

Chalk River Laboratories, Atomic Energy of Canada Limited (AECL), Chalk River ON, K0J 1P0, Canadamohanya@aecl.ca

Department of Mechanical Engineering, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4L7, Canada

2

Corresponding author.

J. Pressure Vessel Technol 131(2), 021302 (Dec 30, 2008) (9 pages) doi:10.1115/1.3027452 History: Received April 15, 2007; Revised September 03, 2007; Published December 30, 2008

## Abstract

A parametric study has been performed to investigate the effect of cylinder diameter on the acoustic resonance mechanism of two tandem cylinders exposed to cross-flow in a duct. Three spacing ratios corresponding to different flow regimes inside the “proximity interference” region are considered, $L∕D=1.5$, 1.75, and 2.5, where $L$ is the spacing between the cylinders and $D$ is the diameter. For each spacing ratio, six cylinder diameters in the range of $D=7.6–27.5mm$ have been tested. For small diameter cylinders, the acoustic resonance mechanism of the tandem cylinders seems to be similar to that observed for single cylinders; i.e., it occurs near frequency coincidence as the vortex shedding frequency approaches that of an acoustic resonance mode. However, for larger diameter cylinders, the resonance of a given acoustic mode occurs over two different ranges of flow velocity. The first resonance range, the precoincidence resonance, occurs at flow velocities much lower than that of frequency coincidence. The second resonance range, the coincidence resonance, is similar to that observed for single and small diameter tandem cylinders. Interestingly, the observed precoincidence resonance phenomenon is similar to the acoustic resonance mechanism of in-line tube bundles. It is shown that increasing the diameter of the tandem cylinders affects several flow parameters such that the system becomes more susceptible to the precoincidence resonance phenomenon. The occurrence and the intensity of the precoincidence resonance are therefore strongly dependent on the diameter of the cylinders.

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## Figures

Figure 8

Aeroacoustic response of two tandem cylinders. (a) L∕D=1.5, D=18.4mm; (b) L∕D=1.5, D=27.5mm.

Figure 9

Aeroacoustic response of two tandem cylinders. L∕D=2.5; D=19.3mm.

Figure 2

Schematic drawing for the test section. P(λ∕2) and P(3λ∕2) stand for the acoustic pressure distribution of the first and third cross-modes of the duct, respectively.

Figure 3

Typical pressure spectrum for two tandem cylinders. U=41m∕s, L∕D=1.5, and D=12.7mm.

Figure 4

Pressure spectra measured on the top wall for two tandem cylinders. L∕D=1.5; D=12.7mm.

Figure 5

Aeroacoustic response of two tandem cylinders. L∕D=1.5; D=12.7mm.

Figure 6

Comparison of the aeroacoustic response of a single cylinder and two tandem cylinders. ◆, two tandem cylinders with L∕D=1.5; △, single cylinder with D=12.7mm in both cases.

Figure 7

Aeroacoustc response of two tandem cylinders. (a) L∕D=1.75, D=10.8mm; (b) L∕D=2.5, D=7.6mm.

Figure 10

Comparison between the acoustic response of two tandem cylinders with that of in-line tube bundles. ◆, two tandem cylinders with L∕D=2; ◻, in-line tube bundles with XL=2.1 and XT=2.5 from Ziada and Oengoeren (8).

Figure 12

Aeroacoustic response of single cylinders in cross-flow. ▲, D=12.7mm; ○, D=19mm; ◆, D=25.4mm.

Figure 13

Illustration of the effect of cylinder diameter on the shear layer instability

Figure 11

Comparison between the acoustic response of two tandem cylinders with that of in-line tube bundles. ◆, two tandem cylinders with L∕D=2.5; ◻, in-line tube bundles with XL=2.6 and XT=3.0 from Oengoeren and Ziada (8).

Figure 1

The tandem cylinder arrangement with different cylinder diameters and the same spacing ratio

Figure 14

Contours of the normalized pressure for the first acoustic mode of the duct housing two tandem cylinders with L∕D=2.5 and D=25.4mm

Figure 15

Pressure distributions of the first acoustic mode along the top wall for the cases of empty duct and two tandem cylinders with different cylinder diameters: D∕H=0.1 and D=25.4mm. ◇, empty duct; △, cylinder diameter of D; ◼, cylinder diameter of 2D. L∕D=2.5.

Figure 16

Contours of the normalized acoustic particle velocity: (a) L∕D=2.5, D=12.7mm; (b) L=2.5D, D=25.4mm.

Figure 17

Frequency of the first acoustic mode of the duct, fa, as a function of the cylinder diameter for two tandem cylinders, L∕D=2.5. H is the test section height and fo is the frequency of the empty duct that corresponds to D∕H=0.

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