Abstract
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.
Highlights
Investigations of flow past a rotating cylinder have been conducted by many researchers through the theoretical, numerical, and experimental methods
The rotation rate varies from 0 to 19, the mean lift at the subcritical Reynolds number is shown in Fig. 7(a), and the variation of the mean lift of the present study is similar to the two-dimensional results of Tokumaru and Dimotakis (1993) and Chew et al (1995), in whose results the mean lift increases and remains steady with the increase in rotation rate
Scitation.org/journal/adv scitation.org/journal/adv the constant of the mean drag is considered to be determined by the aspect ratio and the constant of the present study is closer to that of the cylinder with the largest aspect ratio
Summary
Investigations of flow past a rotating cylinder have been conducted by many researchers through the theoretical, numerical, and experimental methods. The laminar flow at low Reynolds numbers (Re ≤ 300) of a rotating cylinder was investigated by Stojkovic et al (2002), and their results indicated that Prandtl’s limit could be greatly exceeded, with the increasing rotation rate; the trend for the mean lift is approximately the same as those of Mittal and Kumar (2003) and Bourguet and Lo Jacono (2014) with low Reynolds numbers. The works of flow past a rotating cylinder with a wide range of rotation rates are poor, which are concluded in Fig. 1 (Tokumaru and Dimotakis, 1993; Chew et al, 1995; and Chen and Rheem, 2019), in some of which the investigations of the mean drag are ignored.
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