Bifurcation analysis of the primary instability in the flow around a flexibly mounted circular cylinder. (8th October 2019) - Dolci, Daiane I.; Carmo, Bruno S.
Abstract : The nonlinear character of the primary bifurcation is investigated for the flow around a flexibly mounted circular cylinder. We have considered the cases in which the cylinder can oscillate in the transverse direction only and in both transverse and in-line directions. Low and high values of mass ratio ( m^* =5 and 50) were studied, and reduced velocity ( V_r ) values are chosen inside ( V_r=9 ) and outside ( V_r=5 and V_r=13 ) the lock-in range for low Reynolds numbers. For each combination of m^* and V_r, a global linear stability analysis was applied to find the critical Reynolds number Re_c of the fluid–structure system. For V_r in the lock-in range, the values of Re_c were noticeably less than the critical Reynolds number of the flow around a fixed circular cylinder ( Re_c_047 ). On the other hand, for V_r outside the lock-in range, the values of Re_c were close to Re_c_0 . Next, nonlinear analyses were performed in the vicinity of Re_c for each case. Subcritical character (with hysteresis) was observed for V_r in the lock-in range, while for V_r outside the lock-in region the bifurcations were found to be supercritical (without hysteresis). This shows that when the coupling between the structure and flow is strong, due to the proximity of the natural frequencies of the isolated systems, it significantly changes both the linear and nonlinear responses observed.