Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers

Abstract

579Two fundamental characteristics of the low-Reynolds-number cylinder wake, which have involved considerable debate, are first the existence of discontinuities in the Strouhal-Reynolds number relationship, and secondly the phenomenon of oblique vortex shedding. The present paper shows that both of these characteristics of the wake are directly related to each other, and that both are influenced by the boundary conditions at the ends of the cylinder, even for spans of hundreds of diameters in length. It is found that a Strouhal discontinuity exists, which is not due to any of the previously proposed mechanisms, but instead is caused by a transition from one oblique shedding mode to another oblique mode. This transition is explained by a change from one mode where the central flow over the span matches the end boundary conditions to one where the central flow is unable to match the end conditions. In the latter case, quasi-periodic spectra of the velocity fluctuations appear; these are due to the presence of span wise cells of different frequency. During periods when vortices in neighbouring cells move out of phase with each other, 'vortex dislocations' are observed, and are associated with rather complex vortex linking between the cells. However, by manipulating the end boundary conditions, parallel shedding can be induced, which then results in a completely continuous Strouhal curve. It is also universal in the sense that the oblique-shedding Strouhal data (S 11 ) can be collapsed onto the parallel-shedding Strouhal curve (S 0 ) by the transformation, S 0 = S 11 jcos (), where () is the angle of oblique shedding. Close agreement between measurements in two distinctly different facilities confirms the continuous and universal nature of this Strouhal curve. It is believed that the case of parallel shedding represents truly two-dimensional shedding, and a comparison of Strouhal frequency data is made with several two-dimensional numerical simulations, yielding a large disparity which is not clearly understood. The oblique and parallel modes of vortex shedding are both intrinsic to the flow over a cylinder, and are simply solutions to different problems, because the boundary conditions are different in each case.

Suppression of three-dimensional flow instabilities in tube bundles

“…Note that the Strouhal number of the three-dimensional fixed tube is 1.18. This value is much higher than the experimental value of 0.18 for an isolated tube (Williamson, 1989), but is consistent with the value of 1.25 ± 0.1 found for rotated square tube bundles with P/D = 1.5 by Price et al (1995). 1.5D, twice as close as the spacing of 3D seen in simulations of flow past an isolated cylinder (Persillon and Braza, 1998).…”

“…The wake of an isolated cylinder first becomes three-dimensional at Re ≈ 180 via the formation of regular streamwise vortices with a spacing of about three cylinder diameters [the mode A instability identified by Williamson (1989)]. At Re ≈ 230 a second vortex mode appears [the mode B instability identified by Williamson (1989)], characterized by irregular streamwise vortices with a spacing of one cylinder diameter (Williamson, 1989).…”

“…At Re ≈ 230 a second vortex mode appears [the mode B instability identified by Williamson (1989)], characterized by irregular streamwise vortices with a spacing of one cylinder diameter (Williamson, 1989). As Reynolds number increases further, the wake becomes increasingly complicated (possibly via period-doubling) until it is completely turbulent.…”

Boundary conditions on artificial frontiers for incompressible and compressible Navier-Stokes equations

“…The Reynolds numbers given until the end of the section are the real Reynolds numbers Re = U ∞ l c /ν where the characteristic length l c is taken equal to the diameter of the cylinders. For the well-known test of the flow around a cylinder we find results in very good agreement with the physics [24] as it is shown in Table 1 where various values of the Strouhal number are compared. These tests were performed using as reference flow ( 0) t , 0) which is convenient for this kind of flow at low Reynolds numbers.…”

Three-dimensional Floquet stability analysis of the wake of a circular cylinder

“…Other experimentally measured frequency spectra (e.g. Williamson 1988Williamson , 1989Leweke & Provansal 1994 are, in fact, broad-band at Reynolds numbers just above Re?. This would suggest to the contrary that the flow becomes complex at the onset of three-dimensionality.…”