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Research Papers: Fluid-Structure Interaction

# Numerical Simulation of the Flow-Sound Interaction Mechanisms of a Single and Two-Tandem Cylinders in Cross-Flow

[+] Author and Article Information
A. Mohany1

Department of Mechanical Engineering, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4L7, Canadaatef.mohany@gmail.com

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

1

J. Pressure Vessel Technol 131(3), 031306 (Apr 28, 2009) (11 pages) doi:10.1115/1.3110029 History: Received April 29, 2008; Revised November 30, 2008; Published April 28, 2009

## Abstract

A numerical simulation of the flow-excited acoustic resonance for the case of two-tandem cylinders in cross-flow is performed. The spacing ratio between the cylinders ($L/D=2.5$) is inside the proximity interference region. Similar simulation is performed for the case of a single cylinder. The unsteady flow field is simulated using a finite-volume method. This simulation is then coupled with a finite-element simulation of the resonant sound field, by means of Howe’s theory of aerodynamics sound, to reveal the details of flow-sound interaction mechanisms, including the nature and the locations of the aeroacoustic sources in the flow field. For the case of a single cylinder, acoustic resonance is excited over a single range of flow velocity. The main aeroacoustic source, which causes a positive energy transfer from the flow field to the acoustic field, is found to be located just downstream of the cylinder. For the case of two-tandem cylinders, the acoustic resonance is excited over two different ranges of flow velocity: the precoincidence and the coincidence resonance ranges. For the coincidence resonance range, the main aeroacoustic source is found to be located just downstream of the downstream cylinder, and the excitation mechanism of this resonance range is found to be similar to that of a single cylinder. However, for the precoincidence resonance range, the primary acoustic source is found to be located in the gap between the cylinders. Moreover, flow visualization of the wake structure for the two-tandem cylinders during acoustic resonance shows that for the precoincidence resonance range there is a phase shift of about 90 deg between the vortex shedding from the upstream and the downstream cylinders, which is different from the coincidence resonance range, where the vortex shedding from both cylinders seems to be in-phase.

## Figures

Figure 1

Aeroacoustic response of a single cylinder in a duct and exposed to cross-flow: (a) test geometry, (b) frequency of vortex shedding, and (c) normalized pressure on the duct wall at the vortex shedding frequency (2)

Figure 2

Aeroacoustic response of two-tandem cylinders in cross-flow: (a) frequency of vortex shedding, and (b) normalized pressure on the duct wall at the vortex shedding frequency; L/D=2.5(2)

Figure 3

Physical interpretation of the triple product

Figure 4

Drag and lift coefficients for a single cylinder at Re=25,000; no acoustic excitation

Figure 5

Vorticity contours behind the single cylinder at Re=25,000 no acoustic excitation

Figure 6

Dependence of the lock-in on the amplitude and frequency of the cross-flow oscillation for the case of a single cylinder: (◆) lock-in, and (○) no lock-in

Figure 7

Vectors of the acoustic particle velocity around the cylinder taken at the maximum upward direction in the acoustic cycle

Figure 8

Phase relationship between the cross-flow oscillation and the lift coefficient on the cylinder: (solid line) cross-flow oscillation in m/s, and (◆) lift force coefficient

Figure 9

Vorticity contours behind a single cylinder at Re=25,000, after applying the cross-flow oscillation. fa/fv=1; v/U=2.5%. The flow structure corresponds to the same time instant as that of Fig. 5.

Figure 10

Measured rms amplitude of the dynamic lift coefficient at the frequency of vortex shedding from a single cylinder in cross-flow. The resonance peak is due to the onset of acoustic resonance at fa=688 Hz and D=15.8 mm(15).

Figure 11

Small region in the simulation domain showing the nodal points of the acoustic and the flow meshes: (△) acoustic nodal points, and (●) flow nodal points

Figure 12

Contours of the vorticity field and the instantaneous acoustic power taken when the acoustic particle velocity is at its maximum in the downward direction. fa/fv=1; (a) vorticity contours, and (b) instantaneous acoustic power.

Figure 13

Acoustic energy over one cycle fa/fv=1

Figure 14

Total energy transfer per cycle at different downstream locations

Figure 15

The cumulative sum of the total acoustic energy in the downstream direction

Figure 16

Drag and lift coefficients on the downstream cylinder for the case of two-tandem cylinders, L/D=2.5, Re=25,000, no acoustic excitation

Figure 17

Vorticity contours behind two-tandem cylinders, L/D=2.5, at Re=25,000 before applying the cross-flow oscillation

Figure 18

Time history of lift coefficient on the upstream and the downstream cylinders for the case of two-tandem cylinders, L/D=2.5, no acoustic excitation: (solid line) downstream cylinder, and (◼) upstream cylinder.

Figure 19

Results of force measurements for two-tandem cylinders with L/D=2.5: (a) rms amplitude of the dynamic lift coefficient at the frequency of vortex shedding and (b) its phase with respect to the acoustic pressure measured on the top wall. D=15.2 mm. The dashed lines indicate the onset of acoustic resonance, which is the beginning of lock-in range. Refs. 3-4.

Figure 20

Vectors of the acoustic particle velocity around tandem cylinders taken at the maximum upward direction in the acoustic cycle

Figure 21

Vorticity contours behind two-tandem cylinders at conditions simulating the coincidence acoustic resonance: L/D=2.5, Re=25,000, and fa/fv=0.8. The flow structure corresponds to the same time instant as that in Fig. 1.

Figure 22

Time history of lift coefficients on the upstream and the downstream cylinders for the case of two-tandem cylinders at conditions simulating the coincidence acoustic resonance: L/D=2.5 and fa/fv=0.8. (Solid line) downstream cylinder; (◼) upstream cylinder.

Figure 23

Phase relationship between the cross-flow oscillation and the lift force coefficient on the downstream cylinder at conditions simulating the coincidence acoustic resonance. (Solid line) cross-flow oscillation in m/s; (◆) lift force coefficient.

Figure 24

Total acoustic energy over one cycle for two-tandem cylinders, L/D=2.5, coincidence acoustic resonance, fa=0.8fv

Figure 25

Total energy transfer per cycle for different downstream locations. Tandem cylinders, L/D=2.5, Re=25,000, fa=0.8fv.

Figure 26

The cumulative sum of the total acoustic energy in the downstream direction. Two-tandem cylinders, L/D=2.5, coincidence acoustic resonance, fa=0.8fv.

Figure 27

Vorticity contours behind two-tandem cylinders, L/D=2.5, at Re=25,000, precoincidence acoustic resonance, and fa=1.2fv. The flow structure corresponds to the same time instant as that in Fig. 1.

Figure 28

Time history of lift coefficients on the upstream and the downstream cylinders for the case of two-tandem cylinders at conditions simulating the precoincidence acoustic resonance: L/D=2.5, Re=25,000, and fa/fv=1.2. (Solid line) downstream cylinder; (◼) upstream cylinder.

Figure 29

Phase relationship between the cross-flow oscillation and the lift force coefficient on the downstream cylinder at conditions simulating the precoincidence acoustic resonance: L/D=2.5, Re=25,000, and fa/fv=1.2; (solid line) cross-flow oscillation in m/s; (◆) lift force coefficient.

Figure 30

Total acoustic energy over one cycle for two-tandem cylinders, L/D=2.5, precoincidence acoustic resonance, fa=1.2fv

Figure 31

Total energy transfer per cycle for different downstream locations

Figure 32

The cumulative sum of the total acoustic energy in the downstream direction. Tandem cylinders, L/D=2.5, precoincidence acoustic resonance, fa=1.2fv.

Figure 33

Schematic layout of the flow visualization setup

Figure 34

Flow visualization over one shedding cycle during the precoincidence acoustic resonance. L/D=2.5; D=19 mm; fa=690 Hz; Vr=7.58; Re=1.89×105.

Figure 35

Flow visualization over one shedding cycle during the coincidence acoustic resonance. L/D=2.5; D=19 mm; fa=690 Hz; Vr=5.08; Re=1.18×105.

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