Dynamics of two flexible hanging-off circular cylinders in staggered configurations

The present paper is addressed to evaluate the hydrodynamic forces and motions experienced by two flexible circular cylinders in staggered arrays which are towed in still water. The cylinders were submerged partially into the still water from a towing carriage as hanging-off vertical cantilevers. Each cylinder has length-to-diameter ratio of 34.4 with low mass ratio (= 1.24). The Reynolds number varied from 27,000 up to 37,800. For examining wake interference effects on the forces and motion of the cylinders in the staggered configuration, a centre to centre longitudinal gap between the upstream and downstream cylinders was fixed by 4D with transverse gaps were varied by 1D, 1.5D, 2D, 2.5D, 3.5D, and 4.5D, respectively. Measurement of the hydrodynamics forces and motions in two, in-line and transverse directions to the flows were performed simultaneously. Frequency of the drag force was found approximately twice the corresponding lift force frequency at the related reduced velocity (Ur) for all cases and the forces frequencies ratio was independent from the Ur and L _T parameters in the range used. For the upstream cylinder, the L _T = 2.5D became a critical value at which the forces coefficients started to jump into the higher values as the L_T increased (L _T > 2.5D). The influence of the wake interference on the inline and transverse amplitudes are gradually getting weaker as L_T increased. Beyond the stagger angle of 41.2° (L_T ≥ 3.5D), the downstream cylinder behaves approximately as the single cylinder one. In the staggered configurations, as the L_T increased, the trajectory patterns in the domain Ur are step by step approaching the characteristics of the single cylinder case; started at the gaps L_T ≥ 4.5D.