Cellular vortex shedding behind a tapered circular cylinder

Vortex shedding behind a tapered circular cylinder with taper ratio 75 placed normal to the inflow has been studied. The Reynolds numbers based on the uniform inflow velocity and the diameter of the cylinder at the wide and narrow ends were 300 and 102, respectively. In the present direct numerical simulation study it was observed that even with a very long time sampling a discrete cellular shedding pattern prevails. This is in contrast to what Parnaudeau [J. Turbulence 8, 13 (2007)] speculated in their tapered cylinder study, where they suggested that with a longer time sampling a diffused cellular pattern might appear. In the present investigation it was found that streamwise vorticity increases as vortex dislocation occurs, an effect also reported by Piccirillo and Van Atta [J. Fluid Mech. 246, 163 (1993)] in their experimental study. Flow visualizations revealed that both modes A and B secondary flow structures coexist along the span of the present tapered cylinder. The wavelength of mode B is in surprisingly good agreement with the experimental value found by Williamson [J. Fluid Mech. 328, 345 (1996)] for uniform circular cylinders. The present numerical calculation revealed a spanwise secondary motion, both in the front stagnation zone and also in the wake of the cylinder. In the front stagnation zone, the secondary flow was driven by a spanwise pressure gradient. The secondary flow pattern in the wake was found to be rather complex. This complex behavior of the secondary motion was attributed to the intrinsic secondary instabilities induced by the transition process itself. This is in contrast to what Parnaudeau [J. Turbulence 8, 13 (2007)] speculated in their tapered cylinder study, where they attributed this to the oblique and cellular vortex shedding. In spite of this secondary flow in the base region, the local formation length in the present tapered cylinder study is in surprisingly good agreement with the results of uniform circular cylinders.