Investigation of vortex-induced vibration of a circular cylinder near a wavy wall with the local domain-free discretization method

Vortex-induced vibration of a circular cylinder in proximity to a stationary wavy wall at a Reynolds number of 150 is investigated, using an immersed boundary method, called the local domain-free discretization method. The cylinder is elastically mounted and can only oscillate in the transverse direction, with a mass ratio of m*=8/π, zero structural damping (ζ=0), and a reduced velocity Ur ranging from 2 to 9. The effects of wave height h/λ and gap ratio G/D between the cylinder bottom and the wavy wall are studied. Results show that the cylinder responses are significantly affected by the wavy wall. For a small G/D, the cylinder response amplitude Aave basically increases with Ur and h/λ due to collisions between the cylinder and the wavy wall. Even though the lock-in region is unclear, Aave is still large at high Ur. The positive vortices on the lower side of the cylinder are obviously suppressed by the wall. At G/D=1, Aave curve exhibits three distinct branches, i.e., “initial,” “upper,” and “lower,” mainly corresponding to “2S,” “2P,” and “2S” vortex shedding modes. Compared with the unbounded case, the lock-in region is narrowed, whereas the vibration is enhanced. For G/D=2, the lower branch turns unobvious. The lock-in region is broadened with a stronger cylinder vibration compared with the unbounded case. The merging between the vortices shed from the cylinder and the induced secondary ones is precluded, giving rise to complex “2S+S” and “2P+S” shedding modes.