Effect of damping on variable added mass and lift of circular cylinders in vortex-induced vibrations

Abstract

Extensive VIV data, collected by the MRELab of the University of Michigan, are analyzed to investigate the effect of damping on added mass and lift. Systematic change of damping and stiffness is enabled by the Vck system, which simulates the mechanical oscillator without including the hydrodynamic load in the closed control loop. The data acquired are in the TrSL3 flow regime, for Reynolds number 25,000<Re<130,000, mass ratio m∗=1.93, damping ratio ζ in the range 0.0158<ζ<0.1758, and spring stiffness k in the range 400N∕m<k<1800N∕m. To find the effect of damping on added mass and lift, three powerful techniques are used: (a) The damping coefficient c∗ introduced by Vandiver in 2012 to replace the mass-damping parameter. (b) The variable added mass method introduced by Vikestad et al. in 2000 modeling VIV as a resonance phenomenon with variable natural frequency due to variable added-mass. (c) The data collected by the Vck system, which eliminates all nonlinear system damping occurring naturally due to friction before adding mathematically accurate linear viscous damping. The main findings of this study are: (1) With variable added mass, the oscillation frequency is about equal to the mean of the damped natural frequency and the phase between force and displacement is about 90°, consistent with resonance in the VIV lock-in range for the damping-ratio values tested. (2) In the entire upper branch range, the time-averaged variable added mass coefficient increases with increasing damping. Before and after the upper branch, increased damping results in decreased added mass. (3) The maximum non-dimensional amplitude, over the entire lock-in range occurring at the end of the upper branch, depends linearly on c∗(A∗=γc∗+δ) with correlation coefficient R2≅0.99.