In-line force modeling for a circular cylinder in oscillatory flow with non-zero mean velocity

Three-dimensional large eddy simulation (LES) of oscillatory flow with non-zero mean velocity around a circular cylinder is carried out at Reynolds number Re = 15000 to investigate the effects of amplitude ratio (AR) and Keulegan-Carpenter (KC) number on wake structure and fluid forces. The applicability of two-term and three-term Morison equations for modeling the time histories of in-line force is examined. The results show that both AR and KC strongly influence the vortex pattern. The drag coefficient (C_d) of Morison equations increases from a small value with KC first and then decreases and converges to the value of mean drag force in steady flow, with a peak presented when the value of AR/KC is around the Strouhal number (St₀) in steady flow because of resonance effect. This tendency is more significant at higher AR values. The three-term Morison equation exhibits better performance in modeling the in-line fluid force when AR/KC > St₀/3, i.e., the oscillation frequency is greater than three times the vortex shedding frequency in steady flow. In addition, the revised KC number is not appropriate for modeling the flow force in oscillatory flow with non-zero mean velocity.