Numerical investigation of oscillatory flow around a step cylinder

The structures with a similar shape to the step cylinder, which consists of one small-diameter cylinder at the top and a coaxial large-diameter cylinder in the middle, are widely used in marine engineering applications. A numerical simulation of the oscillatory flow around a step cylinder has been performed. In this simulation, by adjusting the values of diameter ratio to 1.8, KC number to 2.8, and β to 80, the flow around the small cylinder is set in regime A, while the flow around the large cylinder is set in regime B. A powerful in-house code MGLET (Multi Grid Large Eddy Turbulence) is used as the numerical solver. All of the CFD simulations are performed on the supercomputer Betzy. A numerical simulation of oscillatory flow around a circular cylinder with parameters KC = 2 and β = 200 is carried out to assess the validity of the numerical code MGLET. The simulation results of Morison’s force coefficients CD and CM, the flow patterns, and spacing between Honji vortices are consistent with previous studies which prove that the numerical code MGLET is suitable for the final simulation. To validate the important CFD setup parameters, a series of convergence studies, e.g., the mesh resolution test, the computational domain size test, the time step test, and the geometry test are performed. In the final simulation, the evolution of the flow in regimes A and B is visualized by using the time history of the relative axial (spanwise) velocity w/Um. The results show that the three-dimensionality due to the appearance of the step slightly affects the flow patterns behind the small cylinder, while it has a great impact on the flow around the large cylinder. The flow behind the small cylinder remains its two-dimensional features as it has in regime A around a uniform cylinder. The three-dimensionality near the step leads to instability in Honji vortices around the large cylinder in regime B and finally induces two kinds of long-term phenomenon: appearance and merging of Honji vortex pair. The appearance and merging process of Honji vortex is presented by vorticity isosurfaces ωy = ±0.1. The cause of Honji vortex generation in the present study is instability in Honji vortices due to the lack of half vortex pair. In the present study, a total of 20.5 or 21.5 pairs of Honji vortex are distributed along the axis of the large cylinder. As time goes by, new vortices appear in a pair below the step. One part of the newly generated vortex pair and the already existing Honji vortex form a new pair. The other vortex of the newly generated vortex pair is left alone and continues to induce instability in the rest of the Honji vortices. The merging process of the Honji vortex shows different features on the negative and positive y sides of the large cylinder. On the negative side, as two neighbouring Honji vortex pairs move toward each other, the negative part of the upper pair and the positive part of the lower pair cancel each other completely and the two remaining parts form a new vortex pair. On the positive side, as the upper and lower vortex pairs keep squeezing the middle vortex pair, the middle vortex pair finally disappear due to the cancellation and suppression effect