On the effect of spacing on the vortex-induced vibrations of two tandem cylinders

A spectral element method using Jacobi polynomial bases is employed to study the vortex-induced oscillations of two identical elastically mounted cylinders in tandem arrangement. Three different cylinder spacings, P/D=2.5P/D=2.5, 3.5 and 5.0, are examined in order to identify the effect of spacing on the two-degree-of-freedom oscillations of the cylinders. Computations were conducted in two space dimensions (2-D)—an assumption that is expected to be valid for the Reynolds number, Re=160Re=160, considered. The single cylinder case is also examined at the same flow and structural parameters for reference and comparison. A widening of the range of the response region of the upstream cylinder is observed when the cylinder spacing is decreased. The synchronization curves of the upstream cylinder display a shift on the reduced velocity (VRVR) axis depending on the spacing. The maximum oscillation amplitude of the downstream cylinder increases when the cylinders are brought to a distance that the flow around the corresponding stationary system displays reattachment. There are three significant frequencies at the spectral responses: the shedding frequency of the stationary tandem system (fo**); the shedding frequency of a single cylinder (fo*); and the natural frequency of the mass-spring system describing the dynamics of the cylinders (fNfN). The energy input of the flow on each cylinder is studied in terms of the line integral of the hydrodynamic force yielding the work, the phase angle between force and displacement at the prominent spectral frequency, and finally the lift in phase with velocity.