A wake oscillator with frequency dependent coupling for the modeling of vortex-induced vibration

The aim of this paper is to improve the phenomenological modeling of vortex-induced vibration of an elastically mounted cylinder in fluid flow. To this end an attempt is made to introduce a wake oscillator model that conforms to both the free and forced vibration experiments. This approach is new as in the past wake oscillator models have been tuned to the free vibration experiments only. First, an existing wake oscillator model is improved by properly including the effect of stall and that of the relatively large attack angles in the course of vortex-induced vibration. Then, to comply with the forced vibration experiments, the model is enhanced by introducing frequency dependent coupling. Such a coupling allows reproduction of the measured frequency dependence of the fluid force on the cylinder. The time domain representation of this coupling is a convolution integral. It is found in this paper that if the wake oscillator is modeled with a Van der Pol equation, it is impossible to find one set of frequency dependent coefficients that conforms to the forced vibration experiments at all amplitudes of cylinder motion. Moreover, the frequency dependencies identified for each frequency separately do not seem to satisfy the Kramers–Kronig relations. Based on the above findings, it is concluded that the nonlinearities in the wake oscillator model used in this paper cannot accurately model the results of vortex-induced vibration measurements. The idea proposed in this paper, that a consistent wake oscillator model must conform to the forced vibration experiments as well, is expected to be a powerful tool in the search for the correct nonlinearity.