Discrete-vortex analysis of high Reynolds number flow past a rotating cylinder

Flow past a rotating cylinder is investigated using a two-dimensional discrete vortex simulation method in this study. The simplified Navier–Stokes equation is solved based on the relationship between the surface pressure gradient and the generated surface vortex strength. The Reynolds number based on the cylinder diameter and flow velocity is 105. The non-dimensional rotation rate, α (the ratio of the cylinder surface velocity and flow velocity), is varied between 0 and 19, and four different wake formations (vortex shedding, weak vortex shedding, wake, and rotating wake formations) have been derived by the imposed rotation. The relationship between the hydrodynamics and wake formation is illustrated. Under vortex shedding and weak vortex shedding formations, periodical hydrodynamics is induced. Under wake formation, no gap between the positive-vorticity and negative-vorticity layers results in the steady hydrodynamics. The separation of the rotating wake induces the huge fluctuation of hydrodynamics under rotating wake formation. These are significant for a flow control technique and for the design of ocean and civil engineering structures. With the increasing rotation rate, the variation of mean hydrodynamics has been discussed and the maximum mean hydrodynamics is considered to be decided by the rotation rate. According to these wake formations, the vortex shedding, weak vortex shedding, wake, and rotating wake areas are identified. Combining the initial, increasing, and equivalent areas for mean hydrodynamics, two different area-divisions have been conducted for mean hydrodynamics and the relationship between the two area-divisions has been illustrated. Finally, the disappearance of vortex shedding and variation of the Strouhal number have been discussed in detail. The critical value for the disappearance of vortex shedding is α ≈ 3.5, and the Strouhal number remains steady initially and then decreases.