## Abstract

Vortex shedding behind a stationary T-shaped cylinder in a circular pipe subjected to periodically varying flow was studied at Reynolds numbers between 6.17 × 10^{3} and 2.46 × 10^{4}, whereas the frequency ratio, F_{s}/F_{o}, ranged from 0.29 to 14.64. F_{s} denotes the natural vortex-shedding frequency referred to the mean flow, and F_{o} denotes the frequency of periodically varying flow. By adopting the Hilbert transform to analyse the velocity signals measured, the instantaneous vortex-shedding frequency was obtained. Based on this quantity, one could categorize the vortex-shedding phenomenon observed into three regimes, namely, quasi-steady vortex shedding for F_{s}/F_{o} > 4.37, hysteresis vortex shedding for F_{s}/F_{o} = 1.56-4.37 and non-interactive vortex shedding for 0.29 < F_{s}/F_{o} < 1.56. In the regime of quasi-steady vortex shedding, the instantaneous vortex-shedding frequency follows the periodically varying flow without phase lag. In the regime of hysteresis vortex shedding, the instantaneous vortex-shedding frequency lags behind the periodically varying flow. Phase lag roughly varies linearly with F_{s}/F_{o}. Further, the variations of non-dimensionalized instantaneous vortex-shedding frequencies obtained in the accelerating and decelerating portions of the periodically varying flow are found to depend on F_{s}/F_{o} and ΔU_{0}/Ū_{0}. In the regime of non-interactive vortex shedding, the vortex-shedding frequency tends to vary with the mean velocity of periodically varying flow, excluding the occurrences of primary and secondary lock-on at F_{s}/F_{o} = 0.97-1.03 and 0.495-0.514, respectively.

Original language | English |
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Pages (from-to) | 911-932 |

Number of pages | 22 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 458 |

Issue number | 2020 |

DOIs | |

Publication status | Published - 2002 Apr 8 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)