Instantaneous vortex-shedding behaviour in periodically varying flow

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 × 10³ and 2.46 × 10⁴, 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 ΔU₀/Ū₀. 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.