Response of a circular cylinder wake to superharmonic excitation

Abstract

A systematic numerical analysis is performed for superharmonic excitations in a wake where a circular cylinder is rotationally oscillated in time. Emphasis is placed on identifying the secondary and tertiary lock-on in the forced wakes. The frequency responses are scrutinized by measuring the lift coefficient ( C L ). A direct numerical simulation has been conducted to portray the unsteady dynamics of wake flows behind a circular cylinder. The Reynolds number based on the diameter is Re = 106, and the forcing magnitude is 0.10 [les ] Ω max [les ] 0.40. The tertiary lock-on is observed, where the shedding frequency ( St 0 ) is one third of the forcing frequency ( S f ), i.e. the 1/3 subharmonic lock-on. The phase shift of C L with respect to the forcing frequency is observed. It is similar to that of the primary lock-on. However, in the secondary superharmonic excitation, modulated oscillations are observed, i.e. the lock-on does not exist. As Ω max increases, St 0 is gradually shifted from the natural shedding frequency ( St * 0 ) to lower values. The magnitudes and phases of S f and St 0 are analysed by the phase diagram. The vorticity contours are employed to examine the vortex formation mode against the forcing conditions.