Damping Parameters for flow-induced vibration

A dimensionless damping parameter, c ⁎ = 2 c ω / ρ U 2 , is defined for cylinders experiencing flow-induced vibration. It overcomes the limitations of “mass-damping” parameters, which first came into use in 1955. A review of the history of mass-damping parameters reveals that they have been used in three principal variations, commonly expressed as Sc, SG and α . For spring-mounted rigid cylinders all three forms reduce to a constant times the following dimensionless group, 2 c / π ρ D 2 ω n , where ‘c’ is the structural damping constant per unit length of cylinder and ω n is the natural frequency of the oscillator, including, when so specified, the fluid added mass. All have been used to predict A⁎max=Amax/D, the peak response amplitude for VIV. None are useful at organizing response at reduced velocities away from the peak in response. The proposed alternative, c⁎, may be used to characterize VIV at all reduced velocities in the lock-in range. The simple product of A⁎ and c⁎ is shown to equal CL, the lift coefficient, thus providing a simple method for compiling CL data from free response measurements. Mass-damping parameters are not well-suited to the organization of the response of flexible cylinders in sheared flows or for cylinders equipped with strakes or fairings. c⁎ is well-suited for use with sheared flows or for cylinders with partial coverage of strakes or fairings. Data from three independent sources are used to illustrate the applications of c⁎. It is shown that the method of modal analysis may be used to generalize the application of c⁎ to flexible risers. An example for a riser with partial fairing coverage is presented.