Physical Modeling and Parametric Study on Two-Degree-of-Freedom VIV of A Cylinder near Rigid Wall

Unlike most previous studies on the transverse vortex-induced vibration(VIV) of a cylinder mainly under the wall-free condition (Williamson & Govardhan, 2004), this paper experimentally investigates the vortex-induced vibration of a cylinder with two degrees of freedom near a rigid wall exposed to steady flow. The amplitude and frequency responses of the cylinder are discussed. The lee wake flow patterns of the cylinder undergoing VIV were visualized by employing the hydrogen bubble technique. The effects of the gap-to-diameter ratio (e(0)/D) and the mass ratio on the vibration amplitude and frequency and analyzed. Comparisons of VIV response of the cylinder are made between one degree (only transverse) and two degrees of freedom (streamwise and transverse) and those between the present study and previous ones. The experimental observation indicates that there are two types of streamwise vibration, i.e., the first streamwise vibration (FSV) with small amplitude and the second streamwise vibration (SSV) which coexists with transverse vibration. The vortex shedding pattern for the FSV is approximately symmetric and that for the SSV is alternate. The first streamwise vibration tends to disappear with the decrease of e(0)/D. For the case of large gap-to-diameter ratios (e.g. e(0)/D = 0.54 similar to 1.58), the maximum amplitudes of the second streamwise vibration and transverse one increase with the increasing gap-to-diameter ratio. But for the case of small gap-to-diameter ratios (e.g. e(0)/D = 0.16, 0.23), the vibration amplitude of the cylinder increases slowly at the initial stage (i.e. at small reduced velocity V-r), and across the maximum amplitude it decreases quickly at the last stage (i.e. at larvae V-r). Within the range of the examined small mass ratio (m(x) < 4), both streamwise and transverse vibration amplitude of the cylinder decrease with the increase of mass ratio for the fixed value of V-r. The vibration range (in terms of V-r) tends to widen with the decrease of the mass ratio. In the second streamwise vibration region, the vibration frequency of the cylinder with a small mass ratio (e.g. m(x)* = 1.44) undergoes a jump at a certain V-r. The maximum amplitudes of the transverse vibration for two-degree-of-freedom case is larger than that for one-degree-of-freedom case, but the transverse vibration frequency of the cylinder with two degrees of freedom is lower than that with one degree of freedom (transverse).