### Abstract

This experimental study investigates the effect of imposed rotary oscillation on the flow-induced vibration of a sphere that is elastically mounted in the cross-flow direction, employing simultaneous displacement, force and vorticity measurements. The response is studied over a wide range of forcing parameters, including the frequency ratio f_{R} and velocity ratio α_{R} of the oscillatory forcing, which vary between 0 ≤ f_{R} ≤ 5 and 0 ≤ α_{R} ≤ 2. The effect of another important flow parameter, the reduced velocity, U∗, is also investigated by varying it in small increments between 0 ≤ U∗ ≤ 20, corresponding to the Reynolds number range of 5000 ≲ Re ≲ 30 000. It has been found that when the forcing frequency of the imposed rotary oscillations, f_{r}, is close to the natural frequency of the system, f_{nw}, (so that f_{R} = f_{r}/f_{nw} ∼ 1), the sphere vibrations lock on to f_{r} instead of f_{nw}. This inhibits the normal resonance or lock-in leading to a highly reduced vibration response amplitude. This phenomenon has been termed 'rotary lock-on', and occurs for only a narrow range of f_{R} in the vicinity of f_{R} = 1. When rotary lock-on occurs, the phase difference between the total transverse force coefficient and the sphere displacement, φ_{total}, jumps from 0° (in phase) to 180° (out of phase). A corresponding dip in the total transverse force coefficient C_{y(rms)} is also observed. Outside the lock-on boundaries, a highly modulated amplitude response is observed. Higher velocity ratios (α_{R} ≥ 0.5) are more effective in reducing the vibration response of a sphere to much lower values. The mode I sphere vortex-induced vibration (VIV) response is found to resist suppression, requiring very high velocity ratios (α_{R} > 1.5) to significantly suppress vibrations for the entire range of f_{R} tested. On the other hand, mode II and mode III are suppressed for α_{R} ≥ 1. The width of the lock-on region increases with an increase in α_{R}. Interestingly, a reduction of VIV is also observed in non-lock-on regions for high f_{R} and α_{R} values. For a fixed α_{R}, when U∗ is progressively increased, the response of the sphere is very rich, exhibiting characteristically different vibration responses for different f_{R} values. The phase difference between the imposed rotary oscillation and the sphere displacement φ_{rot} is found to be crucial in determining the response. For selected f_{R} values, the vibration amplitude increases monotonically with an increase in flow velocity, reaching magnitudes much higher than the peak VIV response for a non-rotating sphere. For these cases, the vibrations are always locked to the forcing frequency, and there is a linear decrease in φ_{rot}. Such vibrations have been termed 'rotary-induced vibrations'. The wake measurements in the cross-plane 1.5D downstream of the sphere position reveal that the sphere wake consists of vortex loops, similar to the wake of a sphere without any imposed rotation; however, there is a change in the timing of vortex formation. On the other hand, for high f_{R} values, there is a reduction in the streamwise vorticity, presumably leading to a decreased total transverse force acting on the sphere and resulting in a reduced response.

Original language | English |
---|---|

Pages (from-to) | 703-735 |

Number of pages | 33 |

Journal | Journal of Fluid Mechanics |

Volume | 855 |

DOIs | |

Publication status | Published - 25 Nov 2018 |

### Keywords

- flow-structure interactions
- vortex streets
- wakes

### Cite this

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**The effect of imposed rotary oscillation on the flow-induced vibration of a sphere.** / Sareen, A.; Zhao, J.; Sheridan, J.; Hourigan, K.; Thompson, M. C.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - The effect of imposed rotary oscillation on the flow-induced vibration of a sphere

AU - Sareen, A.

AU - Zhao, J.

AU - Sheridan, J.

AU - Hourigan, K.

AU - Thompson, M. C.

PY - 2018/11/25

Y1 - 2018/11/25

N2 - This experimental study investigates the effect of imposed rotary oscillation on the flow-induced vibration of a sphere that is elastically mounted in the cross-flow direction, employing simultaneous displacement, force and vorticity measurements. The response is studied over a wide range of forcing parameters, including the frequency ratio fR and velocity ratio αR of the oscillatory forcing, which vary between 0 ≤ fR ≤ 5 and 0 ≤ αR ≤ 2. The effect of another important flow parameter, the reduced velocity, U∗, is also investigated by varying it in small increments between 0 ≤ U∗ ≤ 20, corresponding to the Reynolds number range of 5000 ≲ Re ≲ 30 000. It has been found that when the forcing frequency of the imposed rotary oscillations, fr, is close to the natural frequency of the system, fnw, (so that fR = fr/fnw ∼ 1), the sphere vibrations lock on to fr instead of fnw. This inhibits the normal resonance or lock-in leading to a highly reduced vibration response amplitude. This phenomenon has been termed 'rotary lock-on', and occurs for only a narrow range of fR in the vicinity of fR = 1. When rotary lock-on occurs, the phase difference between the total transverse force coefficient and the sphere displacement, φtotal, jumps from 0° (in phase) to 180° (out of phase). A corresponding dip in the total transverse force coefficient Cy(rms) is also observed. Outside the lock-on boundaries, a highly modulated amplitude response is observed. Higher velocity ratios (αR ≥ 0.5) are more effective in reducing the vibration response of a sphere to much lower values. The mode I sphere vortex-induced vibration (VIV) response is found to resist suppression, requiring very high velocity ratios (αR > 1.5) to significantly suppress vibrations for the entire range of fR tested. On the other hand, mode II and mode III are suppressed for αR ≥ 1. The width of the lock-on region increases with an increase in αR. Interestingly, a reduction of VIV is also observed in non-lock-on regions for high fR and αR values. For a fixed αR, when U∗ is progressively increased, the response of the sphere is very rich, exhibiting characteristically different vibration responses for different fR values. The phase difference between the imposed rotary oscillation and the sphere displacement φrot is found to be crucial in determining the response. For selected fR values, the vibration amplitude increases monotonically with an increase in flow velocity, reaching magnitudes much higher than the peak VIV response for a non-rotating sphere. For these cases, the vibrations are always locked to the forcing frequency, and there is a linear decrease in φrot. Such vibrations have been termed 'rotary-induced vibrations'. The wake measurements in the cross-plane 1.5D downstream of the sphere position reveal that the sphere wake consists of vortex loops, similar to the wake of a sphere without any imposed rotation; however, there is a change in the timing of vortex formation. On the other hand, for high fR values, there is a reduction in the streamwise vorticity, presumably leading to a decreased total transverse force acting on the sphere and resulting in a reduced response.

AB - This experimental study investigates the effect of imposed rotary oscillation on the flow-induced vibration of a sphere that is elastically mounted in the cross-flow direction, employing simultaneous displacement, force and vorticity measurements. The response is studied over a wide range of forcing parameters, including the frequency ratio fR and velocity ratio αR of the oscillatory forcing, which vary between 0 ≤ fR ≤ 5 and 0 ≤ αR ≤ 2. The effect of another important flow parameter, the reduced velocity, U∗, is also investigated by varying it in small increments between 0 ≤ U∗ ≤ 20, corresponding to the Reynolds number range of 5000 ≲ Re ≲ 30 000. It has been found that when the forcing frequency of the imposed rotary oscillations, fr, is close to the natural frequency of the system, fnw, (so that fR = fr/fnw ∼ 1), the sphere vibrations lock on to fr instead of fnw. This inhibits the normal resonance or lock-in leading to a highly reduced vibration response amplitude. This phenomenon has been termed 'rotary lock-on', and occurs for only a narrow range of fR in the vicinity of fR = 1. When rotary lock-on occurs, the phase difference between the total transverse force coefficient and the sphere displacement, φtotal, jumps from 0° (in phase) to 180° (out of phase). A corresponding dip in the total transverse force coefficient Cy(rms) is also observed. Outside the lock-on boundaries, a highly modulated amplitude response is observed. Higher velocity ratios (αR ≥ 0.5) are more effective in reducing the vibration response of a sphere to much lower values. The mode I sphere vortex-induced vibration (VIV) response is found to resist suppression, requiring very high velocity ratios (αR > 1.5) to significantly suppress vibrations for the entire range of fR tested. On the other hand, mode II and mode III are suppressed for αR ≥ 1. The width of the lock-on region increases with an increase in αR. Interestingly, a reduction of VIV is also observed in non-lock-on regions for high fR and αR values. For a fixed αR, when U∗ is progressively increased, the response of the sphere is very rich, exhibiting characteristically different vibration responses for different fR values. The phase difference between the imposed rotary oscillation and the sphere displacement φrot is found to be crucial in determining the response. For selected fR values, the vibration amplitude increases monotonically with an increase in flow velocity, reaching magnitudes much higher than the peak VIV response for a non-rotating sphere. For these cases, the vibrations are always locked to the forcing frequency, and there is a linear decrease in φrot. Such vibrations have been termed 'rotary-induced vibrations'. The wake measurements in the cross-plane 1.5D downstream of the sphere position reveal that the sphere wake consists of vortex loops, similar to the wake of a sphere without any imposed rotation; however, there is a change in the timing of vortex formation. On the other hand, for high fR values, there is a reduction in the streamwise vorticity, presumably leading to a decreased total transverse force acting on the sphere and resulting in a reduced response.

KW - flow-structure interactions

KW - vortex streets

KW - wakes

UR - http://www.scopus.com/inward/record.url?scp=85054688061&partnerID=8YFLogxK

U2 - 10.1017/jfm.2018.667

DO - 10.1017/jfm.2018.667

M3 - Article

VL - 855

SP - 703

EP - 735

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -