Wake structures and vortex-induced forces of a controlled in-line vibrating circular cylinder

Abstract A two-dimensional numerical study was performed to investigate wake structures and fluid forces on a circular cylinder with prescribed vibrations in the in-line direction. Reynolds number was fixed at 500, and the SST k-w model was used to simulate turbulence in the flow. A wake map for in-line vibrations, which includes six wake patterns named AS, SS, S(AS), S(2Po), S(P + S) and S(2P), is drawn in the plane of non-dimensional frequency from 0.2 to 0.9 and an amplitude ratio from 0.01 to 0.275. The S(2Po) mode is a newly discovered wake pattern that consists of two pairs of symmetric vortex shedding per cycle. The S(P + S) mode and S(2P) mode follow similar wake patterns as the P + S mode and the 2P mode for cross flow vibrations, and it takes two in-line cycles to complete one S(P + S) or S(2P) vortex shedding cycle. Extensive numerical investigations show that similar wake structures can be produced if the maximum and minimum values of relative velocity between the flow and the vibrating cylinder are kept the same, regardless of the motion directions. One positive excitation coefficient region is observed for the non-dimensional frequency ranging from 0.38 to 0.43, and the peak amplitude ratio of the zero contour line for the excitation coefficient reaches 0.056. The changing sign of energy transfer between flow and structure is not necessarily caused by the change of wake modes, but it results from the changing time of vortex shedding. Typical 'figure eight' profiles are captured for simultaneous values of lift and drag forces within the positive excitation region.