Objective  In order to achieve the accurate prediction of the amplitude response of a vortex-induced vibrating cylinder under the sub-critical Reynolds number, a method for establishing a Cl-A/D (lift coefficient-amplitude ratio)model of the forced vibration of the cylinder by numerical simulation is proposed.

  Methods  Based on the Realizable k-ε model, a two-dimensional numerical simulation of the forced vibration of a cylinder is carried out using the finite volume method. The calculated lift coefficient curves under different amplitude ratios A/D in the range of excitation frequency ratio f_e/f_n=1 are obtained. The lift coefficient corresponding to the maximum vibration velocity of the cylinder is then selected to establish the Cl-A/D model.

  Results  The results show that the overall trend of the Cl-A/D fitting curve is in good agreement with the predicted results of SHEAR7. At the same time, it is found that the "zero lift coefficient" points under each excitation frequency ratio f_e/f_n are all located near the amplitude ratio A/D=0.8, and the wake shedding mode changes around A/D=0.8 from "P+S" to "2P" (P represents a pair of vortex shedding with opposite rotation directions, and S represents a single vortex shedding). In the vortex-induced vibration experiment of a single cylinder, the maximum amplitude when "lock-in" occurs is around 0.8D.

  Conclusions  The amplitude ratio corresponding to the "zero lift coefficient" of the Cl-A/D model of forced vibrating cylinder under sub-critical Reynolds number is consistent with the maximum response amplitude ratio of the cylinder under vortex-induced vibration, and the shedding mode of the wake vortex changes under this amplitude ratio.